Python RigidBody.angular_momentum方法代码示例

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import angular_momentum [as 别名]
def test_pendulum_angular_momentum():
    """Consider a pendulum of length OA = 2a, of mass m as a rigid body of
    center of mass G (OG = a) which turn around (O,z). The angle between the
    reference frame R and the rod is q.  The inertia of the body is I =
    (G,0,ma^2/3,ma^2/3). """

    m, a = symbols('m, a')
    q = dynamicsymbols('q')

    R = ReferenceFrame('R')
    R1 = R.orientnew('R1', 'Axis', [q, R.z])
    R1.set_ang_vel(R, q.diff() * R.z)

    I = inertia(R1, 0, m * a**2 / 3, m * a**2 / 3)

    O = Point('O')

    A = O.locatenew('A', 2*a * R1.x)
    G = O.locatenew('G', a * R1.x)

    S = RigidBody('S', G, R1, m, (I, G))

    O.set_vel(R, 0)
    A.v2pt_theory(O, R, R1)
    G.v2pt_theory(O, R, R1)

    assert (4 * m * a**2 / 3 * q.diff() * R.z -
            S.angular_momentum(O, R).express(R)) == 0

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import angular_momentum [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 RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import angular_momentum [as 别名]
def test_rigidbody3():
    q1, q2, q3, q4 = dynamicsymbols('q1:5')
    p1, p2, p3 = symbols('p1:4')
    m = symbols('m')

    A = ReferenceFrame('A')
    B = A.orientnew('B', 'axis', [q1, A.x])
    O = Point('O')
    O.set_vel(A, q2*A.x + q3*A.y + q4*A.z)
    P = O.locatenew('P', p1*B.x + p2*B.y + p3*B.z)
    I = outer(B.x, B.x)

    rb1 = RigidBody('rb1', P, B, m, (I, P))
    # I_S/O = I_S/S* + I_S*/O
    rb2 = RigidBody('rb2', P, B, m,
                    (I + inertia_of_point_mass(m, P.pos_from(O), B), O))

    assert rb1.central_inertia == rb2.central_inertia
    assert rb1.angular_momentum(O, A) == rb2.angular_momentum(O, A)

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import angular_momentum [as 别名]
# reference frames
A = ReferenceFrame('A')
B = A.orientnew('B', 'body', [q1, q2, q3], 'xyz')

# points B*, O
pB_star = Point('B*')
pB_star.set_vel(A, 0)

# rigidbody B
I_B_Bs = inertia(B, I11, I22, I33)
rbB = RigidBody('rbB', pB_star, B, m, (I_B_Bs, pB_star))

# kinetic energy
K = rbB.kinetic_energy(A) # velocity of point B* is zero
print('K_ω = {0}'.format(msprint(K)))

print('\nSince I11, I22, I33 are the central principal moments of inertia')
print('let I_min = I11, I_max = I33')
I_min = I11
I_max = I33
H = rbB.angular_momentum(pB_star, A)
K_min = dot(H, H) / I_max / 2
K_max = dot(H, H) / I_min / 2
print('K_ω_min = {0}'.format(msprint(K_min)))
print('K_ω_max = {0}'.format(msprint(K_max)))

print('\nI11/I33, I22/I33 =< 1, since I33 >= I11, I22, so K_ω_min <= K_ω')
print('Similarly, I22/I11, I33/I11 >= 1, '
      'since I11 <= I22, I33, so K_ω_max >= K_ω')

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import angular_momentum [as 别名]
pA = Point('A')
pA.set_vel(N, 0)
pA.set_vel(F1, 0)

# bearing B, center of mass of disc
pB = pA.locatenew('pB', -R*F1.y)
pB.set_vel(B, 0)
pB.v2pt_theory(pA, N, F1)
print('v_B_N = {}'.format(msprint(pB.vel(N))))

Ixx = m*r**2/4
Iyy = m*r**2/4
Izz = m*r**2/2
I_disc = inertia(F2, Ixx, Iyy, Izz, 0, 0, 0)
rb_disc = RigidBody('disc', pB, B, m, (I_disc, pB))
H = rb_disc.angular_momentum(pB, N).subs(vals).express(F2).simplify()
print("H about B in frame N = {}".format(msprint(H)))

#2b
# disc/ground contact point
pC = pB.locatenew('pC', -r*F2.y)

fAx, fAy, fAz, fBx, fBy, fBz = symbols('fAx fAy fAz fBx fBy fBz')
fCx, fCy, fCz = symbols('fCx fCy fCz')
mAx, mAy, mAz, mBx, mBy, mBz = symbols('mAx mAy mAz mBx mBy mBz')

# forces on rod, disc
fA = fAx*F1.x + fAy*F1.y + fAz*F1.z # force exerted on rod at point A
fB = fBx*F2.x + fBy*F2.y + fBz*F2.z # force exerted on disc by rod at point B
fC = fCx*F2.x + fCy*F2.y + fCz*F2.z # force exerted on ground by disc at point C
mA = mAx*F1.x + mAy*F1.y + mAz*F1.z # moment exerted on rod A from axis

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import angular_momentum [as 别名]
q1dd, q2dd = dynamicsymbols('q1 q2', 2)
m, Ia, It = symbols('m Ia It', real=True, positive=True)

N = ReferenceFrame('N')
F = N.orientnew('F', 'axis', [q1, N.z]) # gimbal frame
B = F.orientnew('B', 'axis', [q2, F.x]) # flywheel frame

P = Point('P')
P.set_vel(N, 0)
P.set_vel(F, 0)
P.set_vel(B, 0)

I = inertia(F, Ia, It, It, 0, 0, 0)
rb = RigidBody('flywheel', P, B, m, (I, P))

H = rb.angular_momentum(P, N)
print('H_P_N = {}\n    = {}'.format(H.express(N), H.express(F)))
dH = H.dt(N)
print('d^N(H_P_N)/dt = {}'.format(dH.express(F).subs(q2dd, 0)))

print('\ndH/dt = M')
print('M = {}'.format(dH.express(F).subs(q2dd, 0)))

print('\ncalculation using euler angles')
t = symbols('t')
omega = F.ang_vel_in(N)
wx = omega & F.x
wy = omega & F.y
wz = omega & F.z
s = B.ang_vel_in(F) & F.x
Mx = Ia*(wx + s).diff(t)

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import angular_momentum [as 别名]
from sympy import pi, solve, symbols, simplify
from sympy import acos, sin, cos


# 2a
q1 = dynamicsymbols('q1')

px, py, pz = symbols('px py pz', real=True, positive=True)
sx, sy, sz = symbols('sx sy sz', real=True, sositive=True)
m, g, l0, k = symbols('m g l0 k', real=True, positive=True)
Ixx, Iyy, Izz = symbols('Ixx Iyy Izz', real=True, positive=True)

N = ReferenceFrame('N')
B = N.orientnew('B', 'axis', [q1, N.z])

pA = Point('A')
pA.set_vel(N, 0)

pP = pA.locatenew('P', l0*N.y - 2*l0*N.z)

pS = pP.locatenew('S', -px*B.x - pz*B.z)

I = inertia(B, Ixx, Iyy, Izz, 0, 0, 0)
rb = RigidBody('plane', pS, B, m, (I, pS))
H = rb.angular_momentum(pS, N)
print('H about S in frame N = {}'.format(msprint(H)))
print('dH/dt = {}'.format(msprint(H.dt(N))))

print('a_S_N = {}'.format(pS.acc(N)))