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- from sympy.core.backend 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
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