python from sympy.physics.mechanics import dynamicsymbols from sympy import symbols from sympy.physics.mechanics import ReferenceFrame, Point, Particle from sympy.physics.mechanics import RigidBody, KanesMethod m, g, L, t = symbols('m g L t') x = dynamicsymbols('x') N = ReferenceFrame("N") P = Point("P") P.set_vel(N, 0) A = N.orientnew("A", "Axis", [x, N.z]) A.set_ang_vel(N, x.diff(t) * N.z) Pa = Particle("Pa", P, m) Pa.set_masscenter(P) Pa.mass = m I = m * L**2 / 12 rigid_body = RigidBody("rigid_body", P, A, Pa, (I, P)) gravitational_force = (P, -m * g * N.y) kane = KanesMethod(N, q_ind=[x], u_ind=[x.diff(t)], kd_eqs=[x - L/2], q_dependent=[x.diff(t)], configuration_constraints=[x - L/2]) bodies = [rigid_body] forces = [gravitational_force] fr, fr_star = kane.kanes_equations(forces, bodies) kane.mass_matrix_full kane.forcing_full kane.linearize()