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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
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