test_kane.py 文件源码

def test_pend():
    q, u = dynamicsymbols('q u')
    qd, ud = dynamicsymbols('q u', 1)
    m, l, g = symbols('m l g')
    N = ReferenceFrame('N')
    P = Point('P')
    P.set_vel(N, -l * u * sin(q) * N.x + l * u * cos(q) * N.y)
    kd = [qd - u]

    FL = [(P, m * g * N.x)]
    pa = Particle('pa', P, m)
    BL = [pa]

    KM = KanesMethod(N, [q], [u], kd)
    with warnings.catch_warnings():
        warnings.filterwarnings("ignore", category=SymPyDeprecationWarning)
        KM.kanes_equations(FL, BL)
    MM = KM.mass_matrix
    forcing = KM.forcing
    rhs = MM.inv() * forcing
    rhs.simplify()
    assert expand(rhs[0]) == expand(-g / l * sin(q))
    assert simplify(KM.rhs() -
                    KM.mass_matrix_full.LUsolve(KM.forcing_full)) == zeros(2, 1)