For what it is worth:
With *KM.auxiliary_eqs*
one gets the forces acting on, say, the point where some multi body system
is attached to.
I tried to see, if one could also get the forces needed to make a particle
move in on predetermined path.
In the simple example attached (where the result is obvious), it gives the
correct result.
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#!/usr/bin/env python
# coding: utf-8
# In[2]:
from sympy.physics.mechanics import *
import sympy as sm
from sympy import symbols, Matrix, solve
# simple example to see whether with KM.auxiliary_eqs one can also get the forces needed to move a body
# in a predefined way. At least in the example the result is what one would expect.
#select body or particle
koerper = True # True = body
M = ReferenceFrame('M')
P0 = Point('P0')
P0.set_vel(M, 0)
q1, q2, u1, u2 = dynamicsymbols('q1, q2, u1, u2')
qd1, qd2 = dynamicsymbols('q1, q2', 1)
aux, f1 = dynamicsymbols('aux f1')
iXX, iYY, iZZ = symbols('iXX, iYY, iZZ')
m, g, l, reibung = symbols('m g l reibung')
t = symbols('t')
func = sm.Function('func') #This is the 'forced' position of P1 as a function if time. f1 needed to
func = sm.S(1) - sm.cos(t) #realise this path is the goal.
A = M.orientnew('A', 'Axis', [q1, M.y])
A.set_ang_vel(M, u1*M.y)
hilfs = P0.locatenew('hilfs', l*A.x) #needed to get the correct speed of P1
hilfs.v2pt_theory(P0, M, A)
P1 = hilfs.locatenew('P1', func*A.x)
P1.set_vel(M, hilfs.vel(M) + u2*A.x + aux*A.x)
if koerper:
I = inertia(A, iXX, iYY, iZZ)
P1a = RigidBody('P1a', P1, A, m, (I, P1))
BODY = [P1a]
else:
P1a = Particle('P1a', P1, m)
BODY = [P1a]
FL = [(P1, -m*g*M.y -reibung*u2*A.x + f1*A.x)]
q = [q1, q2]
u = [u1]
u_dep = [u2]
speed_constr = [u2 - func.diff(t)]
kd = [u1 - qd1, u2 - qd2]
aux = [aux]
KM = KanesMethod(M, q_ind=q, u_ind=u, u_dependent=u_dep, kd_eqs=kd, u_auxiliary=aux, velocity_constraints=speed_constr)
fr, frstar = KM.kanes_equations(BODY, FL)
MM = KM.mass_matrix_full
force = KM.forcing_full
print('det(MM) = ', sm.det(MM))
rhs = KM.rhs()
eingepraegt = KM.auxiliary_eqs
eingepraegt = sm.solve(eingepraegt, f1)[f1].subs({u2.diff(t): rhs[3]})
print('force to ensure given motion of P1:', eingepraegt, '\n')
print('rhs:')
rhs
# In[ ]:
