Rigid body dynamics The result is a set of m equations of motion that define the dynamics of the rigid body system. If the generalized forces Q are derivable from a potential energy V(q...,q), then these equations of motion take the form In this case, introduce the Lagrangian, L=T-V, so these equations of motion become These are known as Lagrange's equations of motion. The linear and angular momentum of a rigid system of particles is formulated by measuring the position and velocity of the particles relative to the center of mass. Let the system of particles P, i=1...,n be located at the coordinates
Escape velocity kg or 1,000 kg; what differs is the amount of energy required. For an object of mass formula_9 the energy required to escape the Earth's gravitational field is "GMm / r", a function of the object's mass (where "r" is the radius of the Earth, "G" is the gravitational constant, and "M" is the mass of the Earth, ). A related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object has reached escape velocity when the specific orbital energy is greater or equal to zero. An