<s> """<STR_LIT>""" <EOL> from __future__ import division <EOL> from sympy import expand , sin , cos , solve , symbols , trigsimp , together <EOL> from sympy . physics . mechanics import ReferenceFrame , Point , Particle <EOL> from sympy . physics . mechanics import dot , dynamicsymbols , msprint <EOL> from util import generalized_inertia_forces , generalized_inertia_forces_K <EOL> from util import partial_velocities <EOL> q1 , q2 , q3 = q = dynamicsymbols ( '<STR_LIT>' ) <EOL> q1d , q2d , q3d = qd = dynamicsymbols ( '<STR_LIT>' , level = <NUM_LIT:1> ) <EOL> u1 , u2 , u3 = u = dynamicsymbols ( '<STR_LIT>' ) <EOL> g , m , L , t = symbols ( '<STR_LIT>' ) <EOL> Q , R , S = symbols ( '<STR_LIT>' ) <EOL> N = ReferenceFrame ( '<STR_LIT:N>' ) <EOL> pO = Point ( '<STR_LIT:O>' ) <EOL> pO . set_vel ( N , <NUM_LIT:0> ) <EOL> pP1 = pO . locatenew ( '<STR_LIT>' , L / <NUM_LIT:2> * ( cos ( q1 ) * N . x + sin ( q1 ) * N . y ) ) <EOL> pP2 = pP1 . locatenew ( '<STR_LIT>' , L / <NUM_LIT:2> * ( cos ( q1 ) * N . x + sin ( q1 ) * N . y ) ) <EOL> pP3 = pP2 . locatenew ( '<STR_LIT>' , L / <NUM_LIT:2> * ( cos ( q2 ) * N . x - sin ( q2 ) * N . y ) ) <EOL> pP4 = pP3 . locatenew ( '<STR_LIT>' , L / <NUM_LIT:2> * ( cos ( q2 ) * N . x - sin ( q2 ) * N . y ) ) <EOL> pP5 = pP4 . locatenew ( '<STR_LIT>' , L / <NUM_LIT:2> * ( cos ( q3 ) * N . x + sin ( q3 ) * N . y ) ) <EOL> pP6 = pP5 . locatenew ( '<STR_LIT>' , L / <NUM_LIT:2> * ( cos ( q3 ) * N . x + sin ( q3 ) * N . y ) ) <EOL> points = [ pP1 , pP2 , pP3 , pP4 , pP5 , pP6 ] <EOL> for p in points : <EOL> p . set_vel ( N , p . pos_from ( pO ) . diff ( t , N ) ) <EOL> kde = [ u1 - L * q1d , u2 - L * q2d , u3 - L * q3d ] <EOL> kde_map = solve ( kde , qd ) <EOL> for k , v in kde_map . items ( ) : <EOL> kde_map [ k . diff ( t ) ] = v . diff ( t ) <EOL> forces = [ ( pP1 , <NUM_LIT:6> * m * g * N . x ) , <EOL> ( pP2 , S * N . y + <NUM_LIT:5> * m * g * N . x ) , <EOL> ( pP3 , <NUM_LIT:6> * m * g * N . x ) , <EOL> ( pP4 , - Q * N . y + <NUM_LIT:5> * m * g * N . x ) , <EOL> ( pP5 , <NUM_LIT:6> * m * g * N . x ) , <EOL> ( pP6 , R * N . y + <NUM_LIT:5> * m * g * N . x ) ] <EOL> partials = partial_velocities ( points , u , N , kde_map ) <EOL> system = [ Particle ( '<STR_LIT>' . format ( i ) , p , x * m * g ) <EOL> for i , p , x in zip ( range ( <NUM_LIT:1> , <NUM_LIT:7> ) , points , [ <NUM_LIT:6> , <NUM_LIT:5> ] * <NUM_LIT:3> ) ] <EOL> Fr_star_a , _ = generalized_inertia_forces ( partials , system , kde_map ) <EOL> K = sum ( map ( lambda x : x . kinetic_energy ( N ) , system ) ) <EOL> Fr_star_b = generalized_inertia_forces_K ( K , q , u , kde_map ) <EOL> G = sum ( P . mass * dot ( P . point . acc ( N ) , P . point . acc ( N ) ) <EOL> for P in system ) . subs ( kde_map ) / <NUM_LIT:2> <EOL> Fr_star_c = map ( lambda u_r : - G . diff ( u_r . diff ( t ) ) , u ) <EOL> def print_fr_star ( fr_star ) : <EOL> for i , f in enumerate ( fr_star , <NUM_LIT:1> ) : <EOL> print ( "<STR_LIT>" . format ( i , msprint ( trigsimp ( together ( f ) ) ) ) ) <EOL> print ( '<STR_LIT>' ) <EOL> print_fr_star ( Fr_star_a ) <EOL> print ( '<STR_LIT>' ) <EOL> print_fr_star ( Fr_star_b ) <EOL> print ( '<STR_LIT>' ) <EOL> print_fr_star ( Fr_star_c ) <EOL> for x , y in zip ( Fr_star_a , Fr_star_b ) : <EOL> assert expand ( x - y ) == <NUM_LIT:0> <EOL> for x , y in zip ( Fr_star_a , Fr_star_c ) : <EOL> assert expand ( x - y ) == <NUM_LIT:0> </s>
