<s> """<STR_LIT>""" <EOL> from __future__ import division <EOL> from sympy . physics . mechanics import ReferenceFrame , Point , Particle , RigidBody <EOL> from sympy . physics . mechanics import cross , dot , Vector <EOL> from sympy . physics . mechanics import MechanicsStrPrinter <EOL> from sympy . physics . mechanics import inertia_of_point_mass <EOL> def msprint ( expr ) : <EOL> pr = MechanicsStrPrinter ( ) <EOL> return pr . doprint ( expr ) <EOL> def subs ( x , * args , ** kwargs ) : <EOL> if x == <NUM_LIT:0> : <EOL> return x <EOL> if not hasattr ( x , '<STR_LIT>' ) : <EOL> if hasattr ( x , '<STR_LIT>' ) : <EOL> return map ( lambda x : subs ( x , * args , ** kwargs ) , x ) <EOL> return x . subs ( * args , ** kwargs ) . doit ( ) <EOL> class PartialVelocity ( dict ) : <EOL> def __init__ ( self , frame , ulist , * args , ** kwargs ) : <EOL> self . _set_frame ( frame ) <EOL> self . _set_ulist ( ulist ) <EOL> dict . __init__ ( self , * args , ** kwargs ) <EOL> def _set_frame ( self , f ) : <EOL> if not isinstance ( f , ReferenceFrame ) : <EOL> raise TypeError ( <EOL> '<STR_LIT>' . format ( f ) ) <EOL> self . _frame = f <EOL> def _set_ulist ( self , u ) : <EOL> if not isinstance ( u , list ) : <EOL> raise TypeError ( <EOL> '<STR_LIT>' . format ( f ) ) <EOL> self . _ulist = u <EOL> @ property <EOL> def frame ( self ) : <EOL> return self . _frame <EOL> @ property <EOL> def ulist ( self ) : <EOL> return self . _ulist <EOL> def partial_velocities ( system , generalized_speeds , frame , <EOL> kde_map = None , constraint_map = None , express_frame = None ) : <EOL> partials = PartialVelocity ( frame , generalized_speeds ) <EOL> if express_frame is None : <EOL> express_frame = frame <EOL> for p in system : <EOL> if p in partials : <EOL> continue <EOL> if isinstance ( p , Point ) : <EOL> v = p . vel ( frame ) <EOL> elif isinstance ( p , ReferenceFrame ) : <EOL> v = p . ang_vel_in ( frame ) <EOL> if kde_map is not None : <EOL> v = subs ( v , kde_map ) <EOL> if constraint_map is not None : <EOL> v = subs ( v , constraint_map ) <EOL> v_r_p = { } <EOL> for u in generalized_speeds : <EOL> v_r_p [ u ] = Vector ( [ ] ) if v == <NUM_LIT:0> else v . diff ( u , express_frame ) <EOL> partials [ p ] = v_r_p <EOL> return partials <EOL> def generalized_active_forces ( partials , forces , uaux = None ) : <EOL> ulist = partials . ulist <EOL> if uaux is not None : <EOL> uaux_zero = dict ( zip ( uaux , [ <NUM_LIT:0> ] * len ( uaux ) ) ) <EOL> Fr = [ <NUM_LIT:0> ] * len ( ulist ) <EOL> for pf in forces : <EOL> p = pf [ <NUM_LIT:0> ] <EOL> f = pf [ <NUM_LIT:1> ] <EOL> for i , u in enumerate ( ulist ) : <EOL> if partials [ p ] [ u ] != <NUM_LIT:0> and f != <NUM_LIT:0> : <EOL> r = dot ( partials [ p ] [ u ] , f ) <EOL> if len ( pf ) > <NUM_LIT:2> : <EOL> r = pf [ <NUM_LIT:2> ] ( r ) <EOL> if uaux is not None and u not in uaux : <EOL> r = subs ( r , uaux_zero ) <EOL> Fr [ i ] += r <EOL> return Fr , ulist <EOL> def _calculate_T_star ( rb , frame , kde_map , constraint_map , uaux ) : <EOL> I = rb . inertia [ <NUM_LIT:0> ] - inertia_of_point_mass ( rb . mass , <EOL> rb . masscenter . pos_from ( rb . inertia [ <NUM_LIT:1> ] ) , rb . frame ) <EOL> alpha = rb . frame . ang_acc_in ( frame ) <EOL> omega = rb . frame . ang_vel_in ( frame ) <EOL> if uaux is not None : <EOL> uaux_zero = dict ( zip ( uaux , [ <NUM_LIT:0> ] * len ( uaux ) ) ) <EOL> alpha = subs ( alpha , uaux_zero ) <EOL> omega = subs ( omega , uaux_zero ) <EOL> if kde_map is not None : <EOL> alpha = subs ( alpha , kde_map ) <EOL> omega = subs ( omega , kde_map ) <EOL> if constraint_map is not None : <EOL> alpha = subs ( alpha , constraint_map ) <EOL> omega = subs ( omega , constraint_map ) <EOL> return - dot ( alpha , I ) - dot ( cross ( omega , I ) , omega ) <EOL> def generalized_inertia_forces ( partials , bodies , <EOL> kde_map = None , constraint_map = None , <EOL> uaux = None ) : <EOL> ulist = partials . ulist <EOL> frame = partials . frame <EOL> if uaux is not None : <EOL> uaux_zero = dict ( zip ( uaux , [ <NUM_LIT:0> ] * len ( uaux ) ) ) <EOL> Fr_star = [ <NUM_LIT:0> ] * len ( ulist ) <EOL> for b in bodies : <EOL> if isinstance ( b , RigidBody ) : <EOL> p = b . masscenter <EOL> m = b . mass <EOL> elif isinstance ( b , Particle ) : <EOL> p = b . point <EOL> m = b . mass <EOL> else : <EOL> raise TypeError ( '<STR_LIT>' . format ( b ) ) <EOL> a = p . acc ( frame ) <EOL> if uaux is not None : <EOL> a = subs ( a , uaux_zero ) <EOL> if kde_map is not None : <EOL> a = subs ( a , kde_map ) <EOL> if constraint_map is not None : <EOL> a = subs ( a , constraint_map ) <EOL> if isinstance ( b , RigidBody ) : <EOL> T_star = _calculate_T_star ( b , frame , kde_map , constraint_map , uaux ) <EOL> for i , u in enumerate ( ulist ) : <EOL> force_term = <NUM_LIT:0> <EOL> torque_term = <NUM_LIT:0> <EOL> force_term = dot ( partials [ p ] [ u ] , - m * a ) <EOL> if isinstance ( b , RigidBody ) : <EOL> torque_term = dot ( partials [ b . frame ] [ u ] , T_star ) <EOL> if uaux is not None and u not in uaux : <EOL> force_term = subs ( force_term , uaux_zero ) <EOL> torque_term = subs ( torque_term , uaux_zero ) <EOL> Fr_star [ i ] += force_term + torque_term <EOL> return Fr_star , ulist </s>
