Python Particle.set_potential_energy方法代码示例

# 需要导入模块: from sympy.physics.mechanics import Particle [as 别名]
# 或者: from sympy.physics.mechanics.Particle import set_potential_energy [as 别名]
def test_particle():
    m, m2, v1, v2, v3, r, g, h = symbols('m m2 v1 v2 v3 r g h')
    P = Point('P')
    P2 = Point('P2')
    p = Particle('pa', P, m)
    assert p.mass == m
    assert p.point == P
    # Test the mass setter
    p.mass = m2
    assert p.mass == m2
    # Test the point setter
    p.point = P2
    assert p.point == P2
    # Test the linear momentum function
    N = ReferenceFrame('N')
    O = Point('O')
    P2.set_pos(O, r * N.y)
    P2.set_vel(N, v1 * N.x)
    assert p.linear_momentum(N) == m2 * v1 * N.x
    assert p.angular_momentum(O, N) == -m2 * r *v1 * N.z
    P2.set_vel(N, v2 * N.y)
    assert p.linear_momentum(N) == m2 * v2 * N.y
    assert p.angular_momentum(O, N) == 0
    P2.set_vel(N, v3 * N.z)
    assert p.linear_momentum(N) == m2 * v3 * N.z
    assert p.angular_momentum(O, N) == m2 * r * v3 * N.x
    P2.set_vel(N, v1 * N.x + v2 * N.y + v3 * N.z)
    assert p.linear_momentum(N) == m2 * (v1 * N.x + v2 * N.y + v3 * N.z)
    assert p.angular_momentum(O, N) == m2 * r * (v3 * N.x - v1 * N.z)
    p.set_potential_energy(m * g * h)
    assert p.potential_energy == m * g * h
    # TODO make the result not be system-dependent
    assert p.kinetic_energy(
        N) in [m2*(v1**2 + v2**2 + v3**2)/2,
        m2 * v1**2 / 2 + m2 * v2**2 / 2 + m2 * v3**2 / 2]

# 需要导入模块: from sympy.physics.mechanics import Particle [as 别名]
# 或者: from sympy.physics.mechanics.Particle import set_potential_energy [as 别名]
def test_dub_pen():

    # The system considered is the double pendulum. Like in the
    # test of the simple pendulum above, we begin by creating the generalized
    # coordinates and the simple generalized speeds and accelerations which
    # will be used later. Following this we create frames and points necessary
    # for the kinematics. The procedure isn't explicitly explained as this is
    # similar to the simple  pendulum. Also this is documented on the pydy.org
    # website.
    q1, q2 = dynamicsymbols('q1 q2')
    q1d, q2d = dynamicsymbols('q1 q2', 1)
    q1dd, q2dd = dynamicsymbols('q1 q2', 2)
    u1, u2 = dynamicsymbols('u1 u2')
    u1d, u2d = dynamicsymbols('u1 u2', 1)
    l, m, g = symbols('l m g')

    N = ReferenceFrame('N')
    A = N.orientnew('A', 'Axis', [q1, N.z])
    B = N.orientnew('B', 'Axis', [q2, N.z])

    A.set_ang_vel(N, q1d * A.z)
    B.set_ang_vel(N, q2d * A.z)

    O = Point('O')
    P = O.locatenew('P', l * A.x)
    R = P.locatenew('R', l * B.x)

    O.set_vel(N, 0)
    P.v2pt_theory(O, N, A)
    R.v2pt_theory(P, N, B)

    ParP = Particle('ParP', P, m)
    ParR = Particle('ParR', R, m)

    ParP.set_potential_energy(- m * g * l * cos(q1))
    ParR.set_potential_energy(- m * g * l * cos(q1) - m * g * l * cos(q2))
    L = Lagrangian(N, ParP, ParR)
    lm = LagrangesMethod(L, [q1, q2])
    lm.form_lagranges_equations()

    assert expand(l*m*(2*g*sin(q1) + l*sin(q1)*sin(q2)*q2dd
        + l*sin(q1)*cos(q2)*q2d**2 - l*sin(q2)*cos(q1)*q2d**2
        + l*cos(q1)*cos(q2)*q2dd + 2*l*q1dd) - (simplify(lm.eom[0]))) == 0
    assert expand((l*m*(g*sin(q2) + l*sin(q1)*sin(q2)*q1dd
        - l*sin(q1)*cos(q2)*q1d**2 + l*sin(q2)*cos(q1)*q1d**2
        + l*cos(q1)*cos(q2)*q1dd + l*q2dd)) - (simplify(lm.eom[1]))) == 0

# 需要导入模块: from sympy.physics.mechanics import Particle [as 别名]
# 或者: from sympy.physics.mechanics.Particle import set_potential_energy [as 别名]
def test_potential_energy():
    m, M, l1, g, h, H = symbols('m M l1 g h H')
    omega = dynamicsymbols('omega')
    N = ReferenceFrame('N')
    O = Point('O')
    O.set_vel(N, 0 * N.x)
    Ac = O.locatenew('Ac', l1 * N.x)
    P = Ac.locatenew('P', l1 * N.x)
    a = ReferenceFrame('a')
    a.set_ang_vel(N, omega * N.z)
    Ac.v2pt_theory(O, N, a)
    P.v2pt_theory(O, N, a)
    Pa = Particle('Pa', P, m)
    I = outer(N.z, N.z)
    A = RigidBody('A', Ac, a, M, (I, Ac))
    Pa.set_potential_energy(m * g * h)
    A.set_potential_energy(M * g * H)
    assert potential_energy(A, Pa) == m * g * h + M * g * H

# 需要导入模块: from sympy.physics.mechanics import Particle [as 别名]
# 或者: from sympy.physics.mechanics.Particle import set_potential_energy [as 别名]
def test_simp_pen():
    # This tests that the equations generated by LagrangesMethod are identical
    # to those obtained by hand calculations. The system under consideration is
    # the simple pendulum.
    # We begin by creating the generalized coordinates as per the requirements
    # of LagrangesMethod. Also we created the associate symbols
    # that characterize the system: 'm' is the mass of the bob, l is the length
    # of the massless rigid rod connecting the bob to a point O fixed in the
    # inertial frame.
    q, u = dynamicsymbols('q u')
    qd, ud = dynamicsymbols('q u ', 1)
    l, m, g = symbols('l m g')

    # We then create the inertial frame and a frame attached to the massless
    # string following which we define the inertial angular velocity of the
    # string.
    N = ReferenceFrame('N')
    A = N.orientnew('A', 'Axis', [q, N.z])
    A.set_ang_vel(N, qd * N.z)

    # Next, we create the point O and fix it in the inertial frame. We then
    # locate the point P to which the bob is attached. Its corresponding
    # velocity is then determined by the 'two point formula'.
    O = Point('O')
    O.set_vel(N, 0)
    P = O.locatenew('P', l * A.x)
    P.v2pt_theory(O, N, A)

    # The 'Particle' which represents the bob is then created and its
    # Lagrangian generated.
    Pa = Particle('Pa', P, m)
    Pa.set_potential_energy(- m * g * l * cos(q))
    L = Lagrangian(N, Pa)

    # The 'LagrangesMethod' class is invoked to obtain equations of motion.
    lm = LagrangesMethod(L, [q])
    lm.form_lagranges_equations()
    RHS = lm.rhs()
    assert RHS[1] == -g*sin(q)/l

# 需要导入模块: from sympy.physics.mechanics import Particle [as 别名]
# 或者: from sympy.physics.mechanics.Particle import set_potential_energy [as 别名]
def test_lagrange_2forces():
    ### Equations for two damped springs in serie with two forces

    ### generalized coordinates
    qs = q1, q2 = dynamicsymbols('q1, q2')
    ### generalized speeds
    qds = 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.set_potential_energy(k * q1**2 / 2)

    pP2 = Particle('pP2', P2, m)
    pP2.set_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

# 需要导入模块: from sympy.physics.mechanics import Particle [as 别名]
# 或者: from sympy.physics.mechanics.Particle import set_potential_energy [as 别名]
             g]
#Specified contains the matrix for the input torques
specified = [ankle_torque, waist_torque]

#Specifies numerical constants for inertial/mass properties
#Robot Params
#numerical_constants = array([1.035,  # leg_length[m]
#                             36.754, # leg_mass[kg]
#			     0.85, # body_length[m]
#                             91.61,  # body_mass[kg]
#                             9.81]    # acceleration due to gravity [m/s^2]
#                             )
numerical_constants = array([0.75,
                             7.0,
                             0.5,
                             8.0,
                             9.81])

#Set input torques to 0
numerical_specified = zeros(2)

parameter_dict = dict(zip(constants, numerical_constants))

ke_energy = simplify(kinetic_energy(inertial_frame, waistP, bodyP).subs(parameter_dict))

waistP.set_potential_energy(leg_mass*g*leg_length*cos(theta1))

bodyP.set_potential_energy(body_mass*g*(leg_length*cos(theta1)+body_length*cos(theta1+theta2)))

pe_energy = simplify(potential_energy(waistP, bodyP).subs(parameter_dict))

# 需要导入模块: from sympy.physics.mechanics import Particle [as 别名]
# 或者: from sympy.physics.mechanics.Particle import set_potential_energy [as 别名]
numerical_constants = array([1.0,
                             1.0,
                             1.0,
                             1.0,
                             1.0,
                             1.0,
                             9.81])

#Set input torques to 0
numerical_specified = zeros(3)

parameter_dict = dict(zip(constants, numerical_constants))

ke_energy = simplify(kinetic_energy(inertial_frame, bP, cP, dP))

bP.set_potential_energy(a_mass*g*a_length*cos(theta_a))

cP.set_potential_energy(b_mass*g*(a_length*cos(theta_a)+b_length*cos(theta_a+theta_b)))

dP.set_potential_energy(c_mass*g*(a_length*cos(theta_a)+b_length*cos(theta_a+theta_b)+c_length*cos(theta_a+theta_b+theta_c)))

pe_energy = simplify(potential_energy(bP, cP, dP).subs(parameter_dict))

forcing = simplify(kane.forcing)

mass_matrix = simplify(kane.mass_matrix)

zero_omega = dict(zip(speeds, zeros(3)))

torques = Matrix(specified)

# 需要导入模块: from sympy.physics.mechanics import Particle [as 别名]
# 或者: from sympy.physics.mechanics.Particle import set_potential_energy [as 别名]
# part a
r1 = s*N.x
r2 = (s + l*cos(theta))*N.x + l*sin(theta)*N.y

O = Point('O')
p1 = O.locatenew('p1', r1)
p2 = O.locatenew('p2', r2)

O.set_vel(N, 0)
p1.set_vel(N, p1.pos_from(O).dt(N))
p2.set_vel(N, p2.pos_from(O).dt(N))

P1 = Particle('P1', p1, 2*m)
P2 = Particle('P2', p2, m)

P1.set_potential_energy(0)
P2.set_potential_energy(P2.mass * g * (p2.pos_from(O) & N.y))

L1 = Lagrangian(N, P1, P2)
print('{} = {}'.format('L1', msprint(L1)))

lm1 = LagrangesMethod(L1, [s, theta])
lm1.form_lagranges_equations()
rhs = lm1.rhs()
t = symbols('t')
print('{} = {}'.format(msprint(sd.diff(t)), msprint(rhs[2].simplify())))
print('{} = {}\n'.format(msprint(thetad.diff(t)), msprint(rhs[3].simplify())))

# part b
r1 = s*N.x + h*N.y
r2 = (s + l*cos(theta))*N.x + (h + l*sin(theta))*N.y