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