```python
from sympy import *
init_printing()
```


```python
def skew(l):
    l1, l2, l3 = l
    return Matrix([
        [0, -l3, l2],
        [l3, 0, -l1],
        [-l2, l1, 0]
    ])
```


```python
# define state variables
x, y, z, eta0, eps1, eps2, eps3, u, v, w, p, q, r = symbols('x y z et0 eps1 eps2 eps3 u v w p q r', real=True)
s = Matrix([x, y, z, eta0, eps1, eps2, eps3, u, v, w, p, q, r])

# position and orientation
eta = Matrix([x, y, z, eta0, eps1, eps2, eps3])
nu = Matrix([u, v, w, p, q, r])

# centre of gravity
xg, yg, zg = symbols('xg yg zg', real=True)
rg = Matrix([xg, yg, zg])

# centre of bouyancy
xb, yb, zb = symbols('xb yb zb', real=True)
rb = Matrix([xb, yb, zb])

# center of pressure
xcp, ycp, zcp = symbols('xcp ycp zcp', real=True)
rcp = Matrix([xcp, ycp, zcp])

# mass matrix
m = symbols('m', real=True, positive=True)
Ixx, Iyy, Izz = symbols('Ixx Iyy Izz')
I0 = diag(Ixx, Iyy, Izz)
M = BlockMatrix([
    [m*eye(3), -m*skew(rg)],
    [m*skew(rg), I0]
])
M = Matrix(M)
# M = simplify(M)

# Coriolis and centripetal matrix
nu1 = Matrix([u, v, w])
nu2 = Matrix([p, q, r])
crb = BlockMatrix([
    [zeros(3), -m*skew(nu1)-m*skew(nu2)*skew(rg)],
    [-m*skew(nu1)+m*skew(rg)*skew(nu2), -skew(I0*nu2)]
])
crb = Matrix(crb)
# crb = simplify(crb)

# damping matrix
Xuu, Yvv, Zww, Kpp, Mqq, Nrr = symbols(
    'Xuu Yvv Zww Kpp Mqq Nrr', real=True
)
D = Matrix([
    [Xuu*abs(u), 0, 0, 0, 0, 0],
    [0, Yvv*abs(v), 0, 0, 0, 0],
    [0, 0, Zww*abs(w), 0, 0, 0],
    [0, -zcp*Yvv*abs(v), ycp*Zww*abs(w), Kpp*abs(p), 0, 0],
    [zcp*Xuu*abs(u), 0, -xcp*Zww*abs(w), 0, Mqq*abs(q), 0],
    [-ycp*Xuu*abs(u), xcp*Yvv*abs(v), 0, 0, 0, Nrr*abs(r)]
])
# D = simplify(D)

# rotational transform between body and NED quaternions
Tq = Rational(1,2)*Matrix([
    [-eps1, -eps2, -eps3],
    [eta0, -eps3, eps2],
    [eps3, eta0, -eps1],
    [-eps2, eps1, eta0]
])
# Tq = simplify(Tq)

Rq = Matrix([
    [1-2*(eps2**2+eps3**2), 2*(eps1*eps2-eps3*eta0), 2*(eps1*eps3+eps2*eta0)],
    [2*(eps1*eps2+eps3*eta0), 1-2*(eps1**2+eps3**2), 2*(eps2*eps3-eps1*eta0)],
    [2*(eps1*eps3-eps2*eta0), 2*(eps2*eps3+eps1*eta0), 1-2*(eps1**2+eps2**2)]
])
Jeta = BlockMatrix([
    [Rq, zeros(3)],
    [zeros(4,3), Tq]
])
Jeta = Matrix(Jeta)
# Jeta = simplify(Jeta)

# bouyancy in quaternions
W, B = symbols('W B', real=True)
fg = Matrix([0, 0, W])
fb = Matrix([0, 0, -B])
Rqinv = Rq.inv()
geta = Matrix([
    Rqinv*(fg+fb),
    skew(rg)*Rqinv*fg + skew(rb)*Rqinv*fb
])
# geta = simplify(geta)
```


```python
# print(cse(Jeta))
```


```python
# thrust model
Kt0, Kt1 = symbols('Kt0 Kt1', real=True)
Kt = Matrix([Kt0, Kt1])
Qt0, Qt1 = symbols('Qt0 Qt1', real=True)
Qt = Matrix([Qt0, Qt1])

# control inputs
rpm0, rpm1 = symbols('rpm0 rpm1', real=True)
rpm = Matrix([rpm0, rpm1])
de, dr = symbols('de dr', real=True)
control_vector = Matrix([rpm0, rpm1, de, dr])

# control force vector
Ft = Kt.dot(rpm)
Mt = Qt.dot(rpm)

# coefficient for each element in cost function
tauc = Matrix([
    Ft*cos(de)*cos(dr),
    -Ft*sin(dr),
    Ft*sin(de)*cos(dr),
    Mt*cos(de)*cos(dr),
    -Mt*sin(dr),
    Mt*sin(de)*cos(dr)
])
```


```python
etadot = Jeta*nu
nudot = M.inv()*(tauc - (crb + D)*nu - geta)
```


```python
sdot = Matrix([
   etadot,
   nudot 
])
```


```python
sdot
```




$\displaystyle \left[\begin{matrix}u \left(- 2 eps_{2}^{2} - 2 eps_{3}^{2} + 1\right) + v \left(2 eps_{1} eps_{2} - 2 eps_{3} et_{0}\right) + w \left(2 eps_{1} eps_{3} + 2 eps_{2} et_{0}\right)\\u \left(2 eps_{1} eps_{2} + 2 eps_{3} et_{0}\right) + v \left(- 2 eps_{1}^{2} - 2 eps_{3}^{2} + 1\right) + w \left(- 2 eps_{1} et_{0} + 2 eps_{2} eps_{3}\right)\\u \left(2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right) + v \left(2 eps_{1} et_{0} + 2 eps_{2} eps_{3}\right) + w \left(- 2 eps_{1}^{2} - 2 eps_{2}^{2} + 1\right)\\- \frac{eps_{1} p}{2} - \frac{eps_{2} q}{2} - \frac{eps_{3} r}{2}\\\frac{eps_{2} r}{2} - \frac{eps_{3} q}{2} + \frac{et_{0} p}{2}\\- \frac{eps_{1} r}{2} + \frac{eps_{3} p}{2} + \frac{et_{0} q}{2}\\\frac{eps_{1} q}{2} - \frac{eps_{2} p}{2} + \frac{et_{0} r}{2}\\\frac{\left(- Iyy m xg yg zg + Izz m xg yg zg\right) \left(B \left(\frac{yb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Iyy q r - Izz q r - Kpp p \left|{p}\right| - W \left(\frac{yg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- m q yg - m r zg\right) - v \left(- Yvv zcp \left|{v}\right| + m p yg + m w\right) - w \left(Zww ycp \left|{w}\right| + m p zg - m v\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Ixx Iyy yg - Ixx m xg^{2} yg - Iyy m yg^{3} - Iyy m yg zg^{2}\right) \left(B \left(\frac{xb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Ixx p q - Iyy p q - Nrr r \left|{r}\right| - W \left(\frac{xg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- Xuu ycp \left|{u}\right| + m r xg + m v\right) - v \left(Yvv xcp \left|{v}\right| + m r yg - m u\right) - w \left(- m p xg - m q yg\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx Izz zg + Ixx m xg^{2} zg + Izz m yg^{2} zg + Izz m zg^{3}\right) \left(B \left(- \frac{xb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - Ixx p r + Izz p r - Mqq q \left|{q}\right| - W \left(- \frac{xg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(Xuu zcp \left|{u}\right| + m q xg - m w\right) - v \left(- m p xg - m r zg\right) - w \left(- Zww xcp \left|{w}\right| + m q zg + m u\right) + \left(- Qt_{0} rpm_{0} - Qt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx Iyy xg yg + Ixx m xg^{3} yg + Iyy m xg yg^{3} + Izz m xg yg zg^{2}\right) \left(- Yvv v \left|{v}\right| - p \left(- m p yg - m w\right) - q \left(m p xg + m r zg\right) - r \left(- m r yg + m u\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(- Kt_{0} rpm_{0} - Kt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx Izz xg zg + Ixx m xg^{3} zg + Iyy m xg yg^{2} zg + Izz m xg zg^{3}\right) \left(- Zww w \left|{w}\right| - p \left(- m p zg + m v\right) - q \left(- m q zg - m u\right) - r \left(m p xg + m q yg\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Xuu u \left|{u}\right| - p \left(m q yg + m r zg\right) - q \left(- m q xg + m w\right) - r \left(- m r xg - m v\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right) \left(Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Izz m xg^{2} + Ixx m^{2} xg^{4} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Izz m^{2} xg^{2} zg^{2}\right)}{Ixx Iyy Izz m - Ixx Iyy m^{2} xg^{2} - Ixx Iyy m^{2} yg^{2} - Ixx Izz m^{2} xg^{2} - Ixx Izz m^{2} zg^{2} + Ixx m^{3} xg^{4} + Ixx m^{3} xg^{2} yg^{2} + Ixx m^{3} xg^{2} zg^{2} - Iyy Izz m^{2} yg^{2} - Iyy Izz m^{2} zg^{2} + Iyy m^{3} xg^{2} yg^{2} + Iyy m^{3} yg^{4} + Iyy m^{3} yg^{2} zg^{2} + Izz m^{3} xg^{2} zg^{2} + Izz m^{3} yg^{2} zg^{2} + Izz m^{3} zg^{4}}\\\frac{\left(Ixx m xg yg zg - Izz m xg yg zg\right) \left(B \left(- \frac{xb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - Ixx p r + Izz p r - Mqq q \left|{q}\right| - W \left(- \frac{xg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(Xuu zcp \left|{u}\right| + m q xg - m w\right) - v \left(- m p xg - m r zg\right) - w \left(- Zww xcp \left|{w}\right| + m q zg + m u\right) + \left(- Qt_{0} rpm_{0} - Qt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx Iyy xg + Ixx m xg^{3} + Ixx m xg zg^{2} + Iyy m xg yg^{2}\right) \left(B \left(\frac{xb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Ixx p q - Iyy p q - Nrr r \left|{r}\right| - W \left(\frac{xg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- Xuu ycp \left|{u}\right| + m r xg + m v\right) - v \left(Yvv xcp \left|{v}\right| + m r yg - m u\right) - w \left(- m p xg - m q yg\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Iyy Izz zg - Iyy m yg^{2} zg - Izz m xg^{2} zg - Izz m zg^{3}\right) \left(B \left(\frac{yb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Iyy q r - Izz q r - Kpp p \left|{p}\right| - W \left(\frac{yg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- m q yg - m r zg\right) - v \left(- Yvv zcp \left|{v}\right| + m p yg + m w\right) - w \left(Zww ycp \left|{w}\right| + m p zg - m v\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx Iyy xg yg + Ixx m xg^{3} yg + Iyy m xg yg^{3} + Izz m xg yg zg^{2}\right) \left(- Xuu u \left|{u}\right| - p \left(m q yg + m r zg\right) - q \left(- m q xg + m w\right) - r \left(- m r xg - m v\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Ixx m xg^{2} yg zg - Iyy Izz yg zg + Iyy m yg^{3} zg + Izz m yg zg^{3}\right) \left(- Zww w \left|{w}\right| - p \left(- m p zg + m v\right) - q \left(- m q zg - m u\right) - r \left(m p xg + m q yg\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Yvv v \left|{v}\right| - p \left(- m p yg - m w\right) - q \left(m p xg + m r zg\right) - r \left(- m r yg + m u\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(- Kt_{0} rpm_{0} - Kt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right) \left(Ixx Iyy Izz - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{2} yg^{2} - Iyy Izz m yg^{2} + Iyy m^{2} yg^{4} + Izz m^{2} yg^{2} zg^{2}\right)}{Ixx Iyy Izz m - Ixx Iyy m^{2} xg^{2} - Ixx Iyy m^{2} yg^{2} - Ixx Izz m^{2} xg^{2} - Ixx Izz m^{2} zg^{2} + Ixx m^{3} xg^{4} + Ixx m^{3} xg^{2} yg^{2} + Ixx m^{3} xg^{2} zg^{2} - Iyy Izz m^{2} yg^{2} - Iyy Izz m^{2} zg^{2} + Iyy m^{3} xg^{2} yg^{2} + Iyy m^{3} yg^{4} + Iyy m^{3} yg^{2} zg^{2} + Izz m^{3} xg^{2} zg^{2} + Izz m^{3} yg^{2} zg^{2} + Izz m^{3} zg^{4}}\\\frac{\left(- Ixx m xg yg zg + Iyy m xg yg zg\right) \left(B \left(\frac{xb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Ixx p q - Iyy p q - Nrr r \left|{r}\right| - W \left(\frac{xg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- Xuu ycp \left|{u}\right| + m r xg + m v\right) - v \left(Yvv xcp \left|{v}\right| + m r yg - m u\right) - w \left(- m p xg - m q yg\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Ixx Izz xg - Ixx m xg^{3} - Ixx m xg yg^{2} - Izz m xg zg^{2}\right) \left(B \left(- \frac{xb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - Ixx p r + Izz p r - Mqq q \left|{q}\right| - W \left(- \frac{xg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(Xuu zcp \left|{u}\right| + m q xg - m w\right) - v \left(- m p xg - m r zg\right) - w \left(- Zww xcp \left|{w}\right| + m q zg + m u\right) + \left(- Qt_{0} rpm_{0} - Qt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Iyy Izz yg + Iyy m xg^{2} yg + Iyy m yg^{3} + Izz m yg zg^{2}\right) \left(B \left(\frac{yb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Iyy q r - Izz q r - Kpp p \left|{p}\right| - W \left(\frac{yg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- m q yg - m r zg\right) - v \left(- Yvv zcp \left|{v}\right| + m p yg + m w\right) - w \left(Zww ycp \left|{w}\right| + m p zg - m v\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx Izz xg zg + Ixx m xg^{3} zg + Iyy m xg yg^{2} zg + Izz m xg zg^{3}\right) \left(- Xuu u \left|{u}\right| - p \left(m q yg + m r zg\right) - q \left(- m q xg + m w\right) - r \left(- m r xg - m v\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Ixx m xg^{2} yg zg - Iyy Izz yg zg + Iyy m yg^{3} zg + Izz m yg zg^{3}\right) \left(- Yvv v \left|{v}\right| - p \left(- m p yg - m w\right) - q \left(m p xg + m r zg\right) - r \left(- m r yg + m u\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(- Kt_{0} rpm_{0} - Kt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Zww w \left|{w}\right| - p \left(- m p zg + m v\right) - q \left(- m q zg - m u\right) - r \left(m p xg + m q yg\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right) \left(Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}\right)}{Ixx Iyy Izz m - Ixx Iyy m^{2} xg^{2} - Ixx Iyy m^{2} yg^{2} - Ixx Izz m^{2} xg^{2} - Ixx Izz m^{2} zg^{2} + Ixx m^{3} xg^{4} + Ixx m^{3} xg^{2} yg^{2} + Ixx m^{3} xg^{2} zg^{2} - Iyy Izz m^{2} yg^{2} - Iyy Izz m^{2} zg^{2} + Iyy m^{3} xg^{2} yg^{2} + Iyy m^{3} yg^{4} + Iyy m^{3} yg^{2} zg^{2} + Izz m^{3} xg^{2} zg^{2} + Izz m^{3} yg^{2} zg^{2} + Izz m^{3} zg^{4}}\\\frac{\left(- Iyy m xg yg zg + Izz m xg yg zg\right) \left(- Xuu u \left|{u}\right| - p \left(m q yg + m r zg\right) - q \left(- m q xg + m w\right) - r \left(- m r xg - m v\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Iyy Izz yg + Iyy m xg^{2} yg + Iyy m yg^{3} + Izz m yg zg^{2}\right) \left(- Zww w \left|{w}\right| - p \left(- m p zg + m v\right) - q \left(- m q zg - m u\right) - r \left(m p xg + m q yg\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Iyy Izz zg - Iyy m yg^{2} zg - Izz m xg^{2} zg - Izz m zg^{3}\right) \left(- Yvv v \left|{v}\right| - p \left(- m p yg - m w\right) - q \left(m p xg + m r zg\right) - r \left(- m r yg + m u\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(- Kt_{0} rpm_{0} - Kt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Iyy m xg zg + m^{2} xg^{3} zg + m^{2} xg yg^{2} zg + m^{2} xg zg^{3}\right) \left(B \left(\frac{xb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Ixx p q - Iyy p q - Nrr r \left|{r}\right| - W \left(\frac{xg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- Xuu ycp \left|{u}\right| + m r xg + m v\right) - v \left(Yvv xcp \left|{v}\right| + m r yg - m u\right) - w \left(- m p xg - m q yg\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Izz m xg yg + m^{2} xg^{3} yg + m^{2} xg yg^{3} + m^{2} xg yg zg^{2}\right) \left(B \left(- \frac{xb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - Ixx p r + Izz p r - Mqq q \left|{q}\right| - W \left(- \frac{xg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(Xuu zcp \left|{u}\right| + m q xg - m w\right) - v \left(- m p xg - m r zg\right) - w \left(- Zww xcp \left|{w}\right| + m q zg + m u\right) + \left(- Qt_{0} rpm_{0} - Qt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Iyy Izz - Iyy m xg^{2} - Iyy m yg^{2} - Izz m xg^{2} - Izz m zg^{2} + m^{2} xg^{4} + m^{2} xg^{2} yg^{2} + m^{2} xg^{2} zg^{2}\right) \left(B \left(\frac{yb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Iyy q r - Izz q r - Kpp p \left|{p}\right| - W \left(\frac{yg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- m q yg - m r zg\right) - v \left(- Yvv zcp \left|{v}\right| + m p yg + m w\right) - w \left(Zww ycp \left|{w}\right| + m p zg - m v\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}}\\\frac{\left(Ixx m xg yg zg - Izz m xg yg zg\right) \left(- Yvv v \left|{v}\right| - p \left(- m p yg - m w\right) - q \left(m p xg + m r zg\right) - r \left(- m r yg + m u\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(- Kt_{0} rpm_{0} - Kt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Ixx Izz xg - Ixx m xg^{3} - Ixx m xg yg^{2} - Izz m xg zg^{2}\right) \left(- Zww w \left|{w}\right| - p \left(- m p zg + m v\right) - q \left(- m q zg - m u\right) - r \left(m p xg + m q yg\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx Izz zg + Ixx m xg^{2} zg + Izz m yg^{2} zg + Izz m zg^{3}\right) \left(- Xuu u \left|{u}\right| - p \left(m q yg + m r zg\right) - q \left(- m q xg + m w\right) - r \left(- m r xg - m v\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx m yg zg + m^{2} xg^{2} yg zg + m^{2} yg^{3} zg + m^{2} yg zg^{3}\right) \left(B \left(\frac{xb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Ixx p q - Iyy p q - Nrr r \left|{r}\right| - W \left(\frac{xg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- Xuu ycp \left|{u}\right| + m r xg + m v\right) - v \left(Yvv xcp \left|{v}\right| + m r yg - m u\right) - w \left(- m p xg - m q yg\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Izz m xg yg + m^{2} xg^{3} yg + m^{2} xg yg^{3} + m^{2} xg yg zg^{2}\right) \left(B \left(\frac{yb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Iyy q r - Izz q r - Kpp p \left|{p}\right| - W \left(\frac{yg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- m q yg - m r zg\right) - v \left(- Yvv zcp \left|{v}\right| + m p yg + m w\right) - w \left(Zww ycp \left|{w}\right| + m p zg - m v\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Ixx Izz - Ixx m xg^{2} - Ixx m yg^{2} - Izz m yg^{2} - Izz m zg^{2} + m^{2} xg^{2} yg^{2} + m^{2} yg^{4} + m^{2} yg^{2} zg^{2}\right) \left(B \left(- \frac{xb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - Ixx p r + Izz p r - Mqq q \left|{q}\right| - W \left(- \frac{xg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(Xuu zcp \left|{u}\right| + m q xg - m w\right) - v \left(- m p xg - m r zg\right) - w \left(- Zww xcp \left|{w}\right| + m q zg + m u\right) + \left(- Qt_{0} rpm_{0} - Qt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}}\\\frac{\left(- Ixx m xg yg zg + Iyy m xg yg zg\right) \left(- Zww w \left|{w}\right| - p \left(- m p zg + m v\right) - q \left(- m q zg - m u\right) - r \left(m p xg + m q yg\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx Iyy xg + Ixx m xg^{3} + Ixx m xg zg^{2} + Iyy m xg yg^{2}\right) \left(- Yvv v \left|{v}\right| - p \left(- m p yg - m w\right) - q \left(m p xg + m r zg\right) - r \left(- m r yg + m u\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(- Kt_{0} rpm_{0} - Kt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Ixx Iyy yg - Ixx m xg^{2} yg - Iyy m yg^{3} - Iyy m yg zg^{2}\right) \left(- Xuu u \left|{u}\right| - p \left(m q yg + m r zg\right) - q \left(- m q xg + m w\right) - r \left(- m r xg - m v\right) - \frac{\left(- B + W\right) \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \left(Kt_{0} rpm_{0} + Kt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Ixx m yg zg + m^{2} xg^{2} yg zg + m^{2} yg^{3} zg + m^{2} yg zg^{3}\right) \left(B \left(- \frac{xb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - Ixx p r + Izz p r - Mqq q \left|{q}\right| - W \left(- \frac{xg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} + \frac{zg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(Xuu zcp \left|{u}\right| + m q xg - m w\right) - v \left(- m p xg - m r zg\right) - w \left(- Zww xcp \left|{w}\right| + m q zg + m u\right) + \left(- Qt_{0} rpm_{0} - Qt_{1} rpm_{1}\right) \sin{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(- Iyy m xg zg + m^{2} xg^{3} zg + m^{2} xg yg^{2} zg + m^{2} xg zg^{3}\right) \left(B \left(\frac{yb \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Iyy q r - Izz q r - Kpp p \left|{p}\right| - W \left(\frac{yg \left(4 eps_{1}^{2} eps_{3}^{2} - 2 eps_{1}^{2} + 4 eps_{2}^{2} eps_{3}^{2} - 2 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{zg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- m q yg - m r zg\right) - v \left(- Yvv zcp \left|{v}\right| + m p yg + m w\right) - w \left(Zww ycp \left|{w}\right| + m p zg - m v\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \cos{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}} + \frac{\left(Ixx Iyy - Ixx m xg^{2} - Ixx m zg^{2} - Iyy m yg^{2} - Iyy m zg^{2} + m^{2} xg^{2} zg^{2} + m^{2} yg^{2} zg^{2} + m^{2} zg^{4}\right) \left(B \left(\frac{xb \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yb \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) + Ixx p q - Iyy p q - Nrr r \left|{r}\right| - W \left(\frac{xg \left(4 eps_{1}^{2} eps_{2} eps_{3} + 2 eps_{1} et_{0} + 4 eps_{2}^{3} eps_{3} + 4 eps_{2} eps_{3}^{3} + 4 eps_{2} eps_{3} et_{0}^{2} - 2 eps_{2} eps_{3}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1} - \frac{yg \left(4 eps_{1}^{3} eps_{3} + 4 eps_{1} eps_{2}^{2} eps_{3} + 4 eps_{1} eps_{3}^{3} + 4 eps_{1} eps_{3} et_{0}^{2} - 2 eps_{1} eps_{3} - 2 eps_{2} et_{0}\right)}{4 eps_{1}^{4} + 8 eps_{1}^{2} eps_{2}^{2} + 8 eps_{1}^{2} eps_{3}^{2} + 4 eps_{1}^{2} et_{0}^{2} - 4 eps_{1}^{2} + 4 eps_{2}^{4} + 8 eps_{2}^{2} eps_{3}^{2} + 4 eps_{2}^{2} et_{0}^{2} - 4 eps_{2}^{2} + 4 eps_{3}^{4} + 4 eps_{3}^{2} et_{0}^{2} - 4 eps_{3}^{2} + 1}\right) - u \left(- Xuu ycp \left|{u}\right| + m r xg + m v\right) - v \left(Yvv xcp \left|{v}\right| + m r yg - m u\right) - w \left(- m p xg - m q yg\right) + \left(Qt_{0} rpm_{0} + Qt_{1} rpm_{1}\right) \sin{\left(de \right)} \cos{\left(dr \right)}\right)}{Ixx Iyy Izz - Ixx Iyy m xg^{2} - Ixx Iyy m yg^{2} - Ixx Izz m xg^{2} - Ixx Izz m zg^{2} + Ixx m^{2} xg^{4} + Ixx m^{2} xg^{2} yg^{2} + Ixx m^{2} xg^{2} zg^{2} - Iyy Izz m yg^{2} - Iyy Izz m zg^{2} + Iyy m^{2} xg^{2} yg^{2} + Iyy m^{2} yg^{4} + Iyy m^{2} yg^{2} zg^{2} + Izz m^{2} xg^{2} zg^{2} + Izz m^{2} yg^{2} zg^{2} + Izz m^{2} zg^{4}}\end{matrix}\right]$




```python

```

db0ced147942087e6a276e63ad5afae51731e87c
ipynb
Jupyter Notebook
sam_dynamics/notebooks/dynamics.ipynb
cisprague/sam_common
f477c8bb4fee3d36fe7ff87847833db3b207cf95
BSD-3-Clause
sam_dynamics/notebooks/dynamics.ipynb
cisprague/sam_common
f477c8bb4fee3d36fe7ff87847833db3b207cf95
BSD-3-Clause
sam_dynamics/notebooks/dynamics.ipynb
cisprague/sam_common
f477c8bb4fee3d36fe7ff87847833db3b207cf95
BSD-3-Clause
2021-05-04T09:48:56.000Z
2021-05-04T09:48:56.000Z
Qwen/Qwen-72B
1. YES
2. YES