def test_one_dof(): # This is for a 1 dof spring-mass-damper case. # It is described in more detail in the Kane docstring. q, u = dynamicsymbols('q u') qd, ud = dynamicsymbols('q u', 1) m, c, k = symbols('m c k') N = ReferenceFrame('N') P = Point('P') P.set_vel(N, u * N.x) kd = [qd - u] FL = [(P, (-k * q - c * u) * N.x)] pa = Particle() pa.mass = m pa.point = P BL = [pa] KM = Kane(N) KM.coords([q]) KM.speeds([u]) KM.kindiffeq(kd) KM.kanes_equations(FL, BL) MM = KM.mass_matrix forcing = KM.forcing rhs = MM.inv() * forcing assert expand(rhs[0]) == expand(-(q * k + u * c) / m) assert KM.linearize() == (Matrix([[0, 1], [k, c]]), Matrix([]))
def test_one_dof(): # This is for a 1 dof spring-mass-damper case. # It is described in more detail in the Kane docstring. q, u = dynamicsymbols('q u') qd, ud = dynamicsymbols('q u', 1) m, c, k = symbols('m c k') N = ReferenceFrame('N') P = Point('P') P.set_vel(N, u * N.x) kd = [qd - u] FL = [(P, (-k * q - c * u) * N.x)] pa = Particle('pa', P, m) BL = [pa] KM = Kane(N) KM.coords([q]) KM.speeds([u]) KM.kindiffeq(kd) KM.kanes_equations(FL, BL) MM = KM.mass_matrix forcing = KM.forcing rhs = MM.inv() * forcing assert expand(rhs[0]) == expand(-(q * k + u * c) / m) assert KM.linearize() == (Matrix([[0, 1], [k, c]]), Matrix([]), Matrix([]))