Python ReferenceFrame.set_ang_vel方法代码示例

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_point_funcs():
    q, q2 = dynamicsymbols('q q2')
    qd, q2d = dynamicsymbols('q q2', 1)
    qdd, q2dd = dynamicsymbols('q q2', 2)
    N = ReferenceFrame('N')
    B = ReferenceFrame('B')
    B.set_ang_vel(N, 5 * B.y)
    O = Point('O')
    P = O.locatenew('P', q * B.x)
    assert P.pos_from(O) == q * B.x
    P.set_vel(B, qd * B.x + q2d * B.y)
    assert P.vel(B) == qd * B.x + q2d * B.y
    O.set_vel(N, 0)
    assert O.vel(N) == 0
    assert P.a1pt_theory(O, N, B) == ((-25 * q + qdd) * B.x + (q2dd) * B.y +
                               (-10 * qd) * B.z)

    B = N.orientnew('B', 'Axis', [q, N.z])
    O = Point('O')
    P = O.locatenew('P', 10 * B.x)
    O.set_vel(N, 5 * N.x)
    assert O.vel(N) == 5 * N.x
    assert P.a2pt_theory(O, N, B) == (-10 * qd**2) * B.x + (10 * qdd) * B.y

    B.set_ang_vel(N, 5 * B.y)
    O = Point('O')
    P = O.locatenew('P', q * B.x)
    P.set_vel(B, qd * B.x + q2d * B.y)
    O.set_vel(N, 0)
    assert P.v1pt_theory(O, N, B) == qd * B.x + q2d * B.y - 5 * q * B.z

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_parallel_axis():
    # This is for a 2 dof inverted pendulum on a cart.
    # This tests the parallel axis code in Kane. The inertia of the pendulum is
    # defined about the hinge, not about the center of mass.

    # Defining the constants and knowns of the system
    gravity        = symbols('g')
    k, ls          = symbols('k ls')
    a, mA, mC      = symbols('a mA mC')
    F              = dynamicsymbols('F')
    Ix, Iy, Iz     = symbols('Ix Iy Iz')

    # Declaring the Generalized coordinates and speeds
    q1, q2   = dynamicsymbols('q1 q2')
    q1d, q2d = dynamicsymbols('q1 q2', 1)
    u1, u2   = dynamicsymbols('u1 u2')
    u1d, u2d = dynamicsymbols('u1 u2', 1)

    # Creating reference frames
    N = ReferenceFrame('N')
    A = ReferenceFrame('A')

    A.orient(N, 'Axis', [-q2, N.z])
    A.set_ang_vel(N, -u2 * N.z)

    # Origin of Newtonian reference frame
    O = Point('O')

    # Creating and Locating the positions of the cart, C, and the
    # center of mass of the pendulum, A
    C  = O.locatenew('C',  q1 * N.x)
    Ao = C.locatenew('Ao', a * A.y)

    # Defining velocities of the points
    O.set_vel(N, 0)
    C.set_vel(N, u1 * N.x)
    Ao.v2pt_theory(C, N, A)
    Cart     = Particle('Cart', C, mC)
    Pendulum = RigidBody('Pendulum', Ao, A, mA, (inertia(A, Ix, Iy, Iz), C))

    # kinematical differential equations

    kindiffs  = [q1d - u1, q2d - u2]

    bodyList  = [Cart, Pendulum]

    forceList = [(Ao, -N.y * gravity * mA),
                 (C,  -N.y * gravity * mC),
                 (C,  -N.x * k * (q1 - ls)),
                 (C,   N.x * F)]

    km=Kane(N)
    km.coords([q1, q2])
    km.speeds([u1, u2])
    km.kindiffeq(kindiffs)
    (fr,frstar) = km.kanes_equations(forceList, bodyList)
    mm = km.mass_matrix_full
    assert mm[3, 3] == -Iz

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_parallel_axis():
    # This is for a 2 dof inverted pendulum on a cart.
    # This tests the parallel axis code in KanesMethod. The inertia of the
    # pendulum is defined about the hinge, not about the center of mass.

    # Defining the constants and knowns of the system
    gravity = symbols("g")
    k, ls = symbols("k ls")
    a, mA, mC = symbols("a mA mC")
    F = dynamicsymbols("F")
    Ix, Iy, Iz = symbols("Ix Iy Iz")

    # Declaring the Generalized coordinates and speeds
    q1, q2 = dynamicsymbols("q1 q2")
    q1d, q2d = dynamicsymbols("q1 q2", 1)
    u1, u2 = dynamicsymbols("u1 u2")
    u1d, u2d = dynamicsymbols("u1 u2", 1)

    # Creating reference frames
    N = ReferenceFrame("N")
    A = ReferenceFrame("A")

    A.orient(N, "Axis", [-q2, N.z])
    A.set_ang_vel(N, -u2 * N.z)

    # Origin of Newtonian reference frame
    O = Point("O")

    # Creating and Locating the positions of the cart, C, and the
    # center of mass of the pendulum, A
    C = O.locatenew("C", q1 * N.x)
    Ao = C.locatenew("Ao", a * A.y)

    # Defining velocities of the points
    O.set_vel(N, 0)
    C.set_vel(N, u1 * N.x)
    Ao.v2pt_theory(C, N, A)
    Cart = Particle("Cart", C, mC)
    Pendulum = RigidBody("Pendulum", Ao, A, mA, (inertia(A, Ix, Iy, Iz), C))

    # kinematical differential equations

    kindiffs = [q1d - u1, q2d - u2]

    bodyList = [Cart, Pendulum]

    forceList = [(Ao, -N.y * gravity * mA), (C, -N.y * gravity * mC), (C, -N.x * k * (q1 - ls)), (C, N.x * F)]

    km = KanesMethod(N, [q1, q2], [u1, u2], kindiffs)
    with warnings.catch_warnings():
        warnings.filterwarnings("ignore", category=SymPyDeprecationWarning)
        (fr, frstar) = km.kanes_equations(forceList, bodyList)
    mm = km.mass_matrix_full
    assert mm[3, 3] == Iz

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_rigidbody2():
    M, v, r, omega = dynamicsymbols('M v r omega')
    N = ReferenceFrame('N')
    b = ReferenceFrame('b')
    b.set_ang_vel(N, omega * b.x)
    P = Point('P')
    I = outer (b.x, b.x)
    Inertia_tuple = (I, P)
    B = RigidBody('B', P, b, M, Inertia_tuple)
    P.set_vel(N, v * b.x)
    assert B.angularmomentum(P, N) == omega * b.x
    O = Point('O')
    O.set_vel(N, v * b.x)
    P.set_pos(O, r * b.y)
    assert B.angularmomentum(O, N) == omega * b.x - M*v*r*b.z

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_point_v1pt_theorys():
    q, q2 = dynamicsymbols('q q2')
    qd, q2d = dynamicsymbols('q q2', 1)
    qdd, q2dd = dynamicsymbols('q q2', 2)
    N = ReferenceFrame('N')
    B = ReferenceFrame('B')
    B.set_ang_vel(N, qd * B.z)
    O = Point('O')
    P = O.locatenew('P', B.x)
    P.set_vel(B, 0)
    O.set_vel(N, 0)
    assert P.v1pt_theory(O, N, B) == qd * B.y
    O.set_vel(N, N.x)
    assert P.v1pt_theory(O, N, B) == N.x + qd * B.y
    P.set_vel(B, B.z)
    assert P.v1pt_theory(O, N, B) == B.z + N.x + qd * B.y

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_angular_momentum_and_linear_momentum():
    m, M, l1 = symbols('m M l1')
    q1d = dynamicsymbols('q1d')
    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, q1d * 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))
    assert linear_momentum(N, A, Pa) == 2 * m * q1d* l1 * N.y + M * l1 * q1d * N.y
    assert angular_momentum(O, N, A, Pa) == 4 * m * q1d * l1**2 * N.z + q1d * N.z

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_point_a1pt_theorys():
    q, q2 = dynamicsymbols('q q2')
    qd, q2d = dynamicsymbols('q q2', 1)
    qdd, q2dd = dynamicsymbols('q q2', 2)
    N = ReferenceFrame('N')
    B = ReferenceFrame('B')
    B.set_ang_vel(N, qd * B.z)
    O = Point('O')
    P = O.locatenew('P', B.x)
    P.set_vel(B, 0)
    O.set_vel(N, 0)
    assert P.a1pt_theory(O, N, B) ==  -(qd**2) * B.x + qdd * B.y
    P.set_vel(B, q2d * B.z)
    assert P.a1pt_theory(O, N, B) == -(qd**2) * B.x + qdd * B.y + q2dd * B.z
    O.set_vel(N, q2d * B.x)
    assert P.a1pt_theory(O, N, B) == ((q2dd - qd**2) * B.x + (q2d * qd + qdd) * B.y +
                               q2dd * B.z)

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_kinetic_energy():
    m, M, l1 = symbols('m M l1')
    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))
    assert 0 == kinetic_energy(N, Pa, A) - (M*l1**2*omega**2/2
            + 2*l1**2*m*omega**2 + omega**2/2)

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [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.potential_energy = m * g * h
    A.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 ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_kinetic_energy():
    m, M, l1 = symbols("m M l1")
    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))
    assert 0 == kinetic_energy(N, Pa, A) - (
        M * l1 ** 2 * omega ** 2 / 2 + 2 * l1 ** 2 * m * omega ** 2 + omega ** 2 / 2
    )

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_rigidbody2():
    M, v, r, omega, g, h = dynamicsymbols('M v r omega g h')
    N = ReferenceFrame('N')
    b = ReferenceFrame('b')
    b.set_ang_vel(N, omega * b.x)
    P = Point('P')
    I = outer(b.x, b.x)
    Inertia_tuple = (I, P)
    B = RigidBody('B', P, b, M, Inertia_tuple)
    P.set_vel(N, v * b.x)
    assert B.angular_momentum(P, N) == omega * b.x
    O = Point('O')
    O.set_vel(N, v * b.x)
    P.set_pos(O, r * b.y)
    assert B.angular_momentum(O, N) == omega * b.x - M*v*r*b.z
    B.set_potential_energy(M * g * h)
    assert B.potential_energy == M * g * h
    assert B.kinetic_energy(N) == (omega**2 + M * v**2) / 2

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [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 ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_angular_momentum_and_linear_momentum():
    """A rod with length 2l, centroidal inertia I, and mass M along with a
    particle of mass m fixed to the end of the rod rotate with an angular rate
    of omega about point O which is fixed to the non-particle end of the rod.
    The rod's reference frame is A and the inertial frame is N."""
    m, M, l, I = symbols("m, M, l, I")
    omega = dynamicsymbols("omega")
    N = ReferenceFrame("N")
    a = ReferenceFrame("a")
    O = Point("O")
    Ac = O.locatenew("Ac", l * N.x)
    P = Ac.locatenew("P", l * N.x)
    O.set_vel(N, 0 * N.x)
    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)
    A = RigidBody("A", Ac, a, M, (I * outer(N.z, N.z), Ac))
    expected = 2 * m * omega * l * N.y + M * l * omega * N.y
    assert (linear_momentum(N, A, Pa) - expected) == Vector(0)
    expected = (I + M * l ** 2 + 4 * m * l ** 2) * omega * N.z
    assert (angular_momentum(O, N, A, Pa) - expected).simplify() == Vector(0)

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
def test_angular_momentum_and_linear_momentum():
    """A rod with length 2l, centroidal inertia I, and mass M along with a
    particle of mass m fixed to the end of the rod rotate with an angular rate
    of omega about point O which is fixed to the non-particle end of the rod.
    The rod's reference frame is A and the inertial frame is N."""
    m, M, l, I = symbols('m, M, l, I')
    omega = dynamicsymbols('omega')
    N = ReferenceFrame('N')
    a = ReferenceFrame('a')
    O = Point('O')
    Ac = O.locatenew('Ac', l * N.x)
    P = Ac.locatenew('P', l * N.x)
    O.set_vel(N, 0 * N.x)
    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)
    A = RigidBody('A', Ac, a, M, (I * outer(N.z, N.z), Ac))
    expected = 2 * m * omega * l * N.y + M * l * omega * N.y
    assert linear_momentum(N, A, Pa) == expected
    expected = (I + M * l**2 + 4 * m * l**2) * omega * N.z
    assert angular_momentum(O, N, A, Pa) == expected

# 需要导入模块: from sympy.physics.mechanics import ReferenceFrame [as 别名]
# 或者: from sympy.physics.mechanics.ReferenceFrame import set_ang_vel [as 别名]
from sympy import simplify, symbols
from sympy import sin, cos, pi, integrate, Matrix
from sympy.physics.mechanics import ReferenceFrame, Point, dynamicsymbols
from util import msprint, partial_velocities, generalized_active_forces


## --- Declare symbols ---
u1, u2, u3, u4, u5, u6, u7, u8, u9 = dynamicsymbols('u1:10')
c, R = symbols('c R')
x, y, z, r, phi, theta = symbols('x y z r phi theta')

# --- Reference Frames ---
A = ReferenceFrame('A')
B = ReferenceFrame('B')
C = ReferenceFrame('C')
B.set_ang_vel(A, u1 * B.x + u2 * B.y + u3 * B.z)
C.set_ang_vel(A, u4 * B.x + u5 * B.y + u6 * B.z)
C.set_ang_vel(B, C.ang_vel_in(A) - B.ang_vel_in(A))

pC_star = Point('C*')
pC_star.set_vel(C, 0)
# since radius of cavity is very small, assume C* has zero velocity in B
pC_star.set_vel(B, 0)
pC_star.set_vel(A, u7 * B.x + u8*B.y + u9*B.z)

## --- define points P, P' ---
# point on C
pP = pC_star.locatenew('P', x * B.x + y * B.y + z * B.z)
pP.set_vel(C, 0)
pP.v2pt_theory(pC_star, B, C)
pP.v2pt_theory(pC_star, A, C)