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| from sympy import symbols | |
| from sympy.physics.mechanics import dynamicsymbols | |
| from sympy.physics.mechanics import ReferenceFrame, Point, Particle | |
| from sympy.physics.mechanics import LagrangesMethod, Lagrangian | |
| ### This test asserts that a system with more than one external forces | |
| ### is acurately formed with Lagrange method (see issue #8626) | |
| def test_lagrange_2forces(): | |
| ### Equations for two damped springs in serie with two forces | |
| ### generalized coordinates | |
| q1, q2 = dynamicsymbols('q1, q2') | |
| ### generalized speeds | |
| q1d, q2d = dynamicsymbols('q1, q2', 1) | |
| ### Mass, spring strength, friction coefficient | |
| m, k, nu = symbols('m, k, nu') | |
| N = ReferenceFrame('N') | |
| O = Point('O') | |
| ### Two points | |
| P1 = O.locatenew('P1', q1 * N.x) | |
| P1.set_vel(N, q1d * N.x) | |
| P2 = O.locatenew('P1', q2 * N.x) | |
| P2.set_vel(N, q2d * N.x) | |
| pP1 = Particle('pP1', P1, m) | |
| pP1.potential_energy = k * q1**2 / 2 | |
| pP2 = Particle('pP2', P2, m) | |
| pP2.potential_energy = k * (q1 - q2)**2 / 2 | |
| #### Friction forces | |
| forcelist = [(P1, - nu * q1d * N.x), | |
| (P2, - nu * q2d * N.x)] | |
| lag = Lagrangian(N, pP1, pP2) | |
| l_method = LagrangesMethod(lag, (q1, q2), forcelist=forcelist, frame=N) | |
| l_method.form_lagranges_equations() | |
| eq1 = l_method.eom[0] | |
| assert eq1.diff(q1d) == nu | |
| eq2 = l_method.eom[1] | |
| assert eq2.diff(q2d) == nu | |