本文整理汇总了Python中sympy.physics.mechanics.RigidBody类的典型用法代码示例。如果您正苦于以下问题:Python RigidBody类的具体用法?Python RigidBody怎么用?Python RigidBody使用的例子?那么恭喜您, 这里精选的类代码示例或许可以为您提供帮助。
在下文中一共展示了RigidBody类的15个代码示例,这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞,您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: test_pendulum_angular_momentum
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
示例2: test_aux
def test_aux():
# Same as above, except we have 2 auxiliary speeds for the ground contact
# point, which is known to be zero. In one case, we go through then
# substitute the aux. speeds in at the end (they are zero, as well as their
# derivative), in the other case, we use the built-in auxiliary speed part
# of Kane. The equations from each should be the same.
q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
q1d, q2d, q3d, u1d, u2d, u3d = dynamicsymbols('q1 q2 q3 u1 u2 u3', 1)
u4, u5, f1, f2 = dynamicsymbols('u4, u5, f1, f2')
u4d, u5d = dynamicsymbols('u4, u5', 1)
r, m, g = symbols('r m g')
N = ReferenceFrame('N')
Y = N.orientnew('Y', 'Axis', [q1, N.z])
L = Y.orientnew('L', 'Axis', [q2, Y.x])
R = L.orientnew('R', 'Axis', [q3, L.y])
R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
R.set_ang_acc(N, R.ang_vel_in(N).dt(R) + (R.ang_vel_in(N) ^
R.ang_vel_in(N)))
C = Point('C')
C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
Dmc = C.locatenew('Dmc', r * L.z)
Dmc.v2pt_theory(C, N, R)
Dmc.a2pt_theory(C, N, R)
I = inertia(L, m / 4 * r**2, m / 2 * r**2, m / 4 * r**2)
kd = [q1d - u3/cos(q3), q2d - u1, q3d - u2 + u3 * tan(q2)]
ForceList = [(Dmc, - m * g * Y.z), (C, f1 * L.x + f2 * (Y.z ^ L.x))]
BodyD = RigidBody()
BodyD.mc = Dmc
BodyD.inertia = (I, Dmc)
BodyD.frame = R
BodyD.mass = m
BodyList = [BodyD]
KM = Kane(N)
KM.coords([q1, q2, q3])
KM.speeds([u1, u2, u3, u4, u5])
KM.kindiffeq(kd)
kdd = KM.kindiffdict()
(fr, frstar) = KM.kanes_equations(ForceList, BodyList)
fr = fr.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5:0})
frstar = frstar.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5:0})
KM2 = Kane(N)
KM2.coords([q1, q2, q3])
KM2.speeds([u1, u2, u3], u_auxiliary=[u4, u5])
KM2.kindiffeq(kd)
(fr2, frstar2) = KM2.kanes_equations(ForceList, BodyList)
fr2 = fr2.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5:0})
frstar2 = frstar2.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5:0})
assert fr.expand() == fr2.expand()
assert frstar.expand() == frstar2.expand()
示例3: test_rolling_disc
def test_rolling_disc():
# Rolling Disc Example
# Here the rolling disc is formed from the contact point up, removing the
# need to introduce generalized speeds. Only 3 configuration and 3
# speed variables are need to describe this system, along with the
# disc's mass and radius, and the local gravity.
q1, q2, q3 = dynamicsymbols('q1 q2 q3')
q1d, q2d, q3d = dynamicsymbols('q1 q2 q3', 1)
r, m, g = symbols('r m g')
# The kinematics are formed by a series of simple rotations. Each simple
# rotation creates a new frame, and the next rotation is defined by the new
# frame's basis vectors. This example uses a 3-1-2 series of rotations, or
# Z, X, Y series of rotations. Angular velocity for this is defined using
# the second frame's basis (the lean frame).
N = ReferenceFrame('N')
Y = N.orientnew('Y', 'Axis', [q1, N.z])
L = Y.orientnew('L', 'Axis', [q2, Y.x])
R = L.orientnew('R', 'Axis', [q3, L.y])
# This is the translational kinematics. We create a point with no velocity
# in N; this is the contact point between the disc and ground. Next we form
# the position vector from the contact point to the disc's center of mass.
# Finally we form the velocity and acceleration of the disc.
C = Point('C')
C.set_vel(N, 0)
Dmc = C.locatenew('Dmc', r * L.z)
Dmc.v2pt_theory(C, N, R)
# Forming the inertia dyadic.
I = inertia(L, m / 4 * r**2, m / 2 * r**2, m / 4 * r**2)
BodyD = RigidBody('BodyD', Dmc, R, m, (I, Dmc))
# Finally we form the equations of motion, using the same steps we did
# before. Supply the Lagrangian, the generalized speeds.
BodyD.set_potential_energy(- m * g * r * cos(q2))
Lag = Lagrangian(N, BodyD)
q = [q1, q2, q3]
q1 = Function('q1')
q2 = Function('q2')
q3 = Function('q3')
l = LagrangesMethod(Lag, q)
l.form_lagranges_equations()
RHS = l.rhs()
RHS.simplify()
t = symbols('t')
assert (l.mass_matrix[3:6] == [0, 5*m*r**2/4, 0])
assert RHS[4].simplify() == (-8*g*sin(q2(t)) + 5*r*sin(2*q2(t)
)*Derivative(q1(t), t)**2 + 12*r*cos(q2(t))*Derivative(q1(t), t
)*Derivative(q3(t), t))/(10*r)
assert RHS[5] == (-5*cos(q2(t))*Derivative(q1(t), t) + 6*tan(q2(t)
)*Derivative(q3(t), t) + 4*Derivative(q1(t), t)/cos(q2(t))
)*Derivative(q2(t), t)
示例4: test_rigidbody2
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
示例5: test_disc_on_an_incline_plane
def test_disc_on_an_incline_plane():
# Disc rolling on an inclined plane
# First the generalized coordinates are created. The mass center of the
# disc is located from top vertex of the inclined plane by the generalized
# coordinate 'y'. The orientation of the disc is defined by the angle
# 'theta'. The mass of the disc is 'm' and its radius is 'R'. The length of
# the inclined path is 'l', the angle of inclination is 'alpha'. 'g' is the
# gravitational constant.
y, theta = dynamicsymbols('y theta')
yd, thetad = dynamicsymbols('y theta', 1)
m, g, R, l, alpha = symbols('m g R l alpha')
# Next, we create the inertial reference frame 'N'. A reference frame 'A'
# is attached to the inclined plane. Finally a frame is created which is attached to the disk.
N = ReferenceFrame('N')
A = N.orientnew('A', 'Axis', [pi/2 - alpha, N.z])
B = A.orientnew('B', 'Axis', [-theta, A.z])
# Creating the disc 'D'; we create the point that represents the mass
# center of the disc and set its velocity. The inertia dyadic of the disc
# is created. Finally, we create the disc.
Do = Point('Do')
Do.set_vel(N, yd * A.x)
I = m * R**2 / 2 * B.z | B.z
D = RigidBody('D', Do, B, m, (I, Do))
# To construct the Lagrangian, 'L', of the disc, we determine its kinetic
# and potential energies, T and U, respectively. L is defined as the
# difference between T and U.
D.set_potential_energy(m * g * (l - y) * sin(alpha))
L = Lagrangian(N, D)
# We then create the list of generalized coordinates and constraint
# equations. The constraint arises due to the disc rolling without slip on
# on the inclined path. Also, the constraint is holonomic but we supply the
# differentiated holonomic equation as the 'LagrangesMethod' class requires
# that. We then invoke the 'LagrangesMethod' class and supply it the
# necessary arguments and generate the equations of motion. The'rhs' method
# solves for the q_double_dots (i.e. the second derivative with respect to
# time of the generalized coordinates and the lagrange multiplers.
q = [y, theta]
coneq = [yd - R * thetad]
m = LagrangesMethod(L, q, coneq)
m.form_lagranges_equations()
rhs = m.rhs()
rhs.simplify()
assert rhs[2] == 2*g*sin(alpha)/3
示例6: test_rigidbody
def test_rigidbody():
m, m2, v1, v2, v3, omega = symbols('m m2 v1 v2 v3 omega')
A = ReferenceFrame('A')
A2 = ReferenceFrame('A2')
P = Point('P')
P2 = Point('P2')
I = Dyadic(0)
I2 = Dyadic(0)
B = RigidBody('B', P, A, m, (I, P))
assert B.mass == m
assert B.frame == A
assert B.masscenter == P
assert B.inertia == (I, B.masscenter)
B.mass = m2
B.frame = A2
B.masscenter = P2
B.inertia = (I2, B.masscenter)
raises(TypeError, lambda: RigidBody(P, P, A, m, (I, P)))
raises(TypeError, lambda: RigidBody('B', P, P, m, (I, P)))
raises(TypeError, lambda: RigidBody('B', P, A, m, (P, P)))
raises(TypeError, lambda: RigidBody('B', P, A, m, (I, I)))
assert B.__str__() == 'B'
assert B.mass == m2
assert B.frame == A2
assert B.masscenter == P2
assert B.inertia == (I2, B.masscenter)
assert B.masscenter == P2
assert B.inertia == (I2, B.masscenter)
# Testing linear momentum function assuming A2 is the inertial frame
N = ReferenceFrame('N')
P2.set_vel(N, v1 * N.x + v2 * N.y + v3 * N.z)
assert B.linear_momentum(N) == m2 * (v1 * N.x + v2 * N.y + v3 * N.z)
示例7: test_potential_energy
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
示例8: test_rigidbody2
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.potential_energy = M * g * h
assert B.potential_energy == M * g * h
assert B.kinetic_energy(N) == (omega**2 + M * v**2) / 2
示例9: test_potential_energy
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
示例10: test_rigidbody3
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)
示例11: test_rigidbody
def test_rigidbody():
m = Symbol('m')
A = ReferenceFrame('A')
P = Point('P')
I = Dyadic([])
B = RigidBody()
assert B.mass == None
assert B.mc == None
assert B.inertia == (None, None)
assert B.frame == None
B.mass = m
B.frame = A
B.cm = P
B.inertia = (I, B.cm)
assert B.mass == m
assert B.frame == A
assert B.cm == P
assert B.inertia == (I, B.cm)
示例12: __init__
def __init__(self, name, masscenter=None, mass=None, frame=None,
central_inertia=None):
self.name = name
self.loads = []
if frame is None:
frame = ReferenceFrame(name + '_frame')
if masscenter is None:
masscenter = Point(name + '_masscenter')
if central_inertia is None and mass is None:
ixx = Symbol(name + '_ixx')
iyy = Symbol(name + '_iyy')
izz = Symbol(name + '_izz')
izx = Symbol(name + '_izx')
ixy = Symbol(name + '_ixy')
iyz = Symbol(name + '_iyz')
_inertia = (inertia(frame, ixx, iyy, izz, ixy, iyz, izx),
masscenter)
else:
_inertia = (central_inertia, masscenter)
if mass is None:
_mass = Symbol(name + '_mass')
else:
_mass = mass
masscenter.set_vel(frame, 0)
# If user passes masscenter and mass then a particle is created
# otherwise a rigidbody. As a result a body may or may not have inertia.
if central_inertia is None and mass is not None:
self.frame = frame
self.masscenter = masscenter
Particle.__init__(self, name, masscenter, _mass)
else:
RigidBody.__init__(self, name, masscenter, frame, _mass, _inertia)
示例13: test_rigidbody
def test_rigidbody():
m, m2 = symbols('m m2')
A = ReferenceFrame('A')
A2 = ReferenceFrame('A2')
P = Point('P')
P2 = Point('P2')
I = Dyadic([])
I2 = Dyadic([])
B = RigidBody('B', P, A, m, (I, P))
assert B.mass == m
assert B.frame == A
assert B.mc == P
assert B.inertia == (I, B.mc)
B.mass = m2
B.frame = A2
B.mc = P2
B.inertia = (I2, B.mc)
assert B.mass == m2
assert B.frame == A2
assert B.mc == P2
assert B.inertia == (I2, B.mc)
示例14: test_linearize_rolling_disc_lagrange
def test_linearize_rolling_disc_lagrange():
q1, q2, q3 = q = dynamicsymbols("q1 q2 q3")
q1d, q2d, q3d = qd = dynamicsymbols("q1 q2 q3", 1)
r, m, g = symbols("r m g")
N = ReferenceFrame("N")
Y = N.orientnew("Y", "Axis", [q1, N.z])
L = Y.orientnew("L", "Axis", [q2, Y.x])
R = L.orientnew("R", "Axis", [q3, L.y])
C = Point("C")
C.set_vel(N, 0)
Dmc = C.locatenew("Dmc", r * L.z)
Dmc.v2pt_theory(C, N, R)
I = inertia(L, m / 4 * r ** 2, m / 2 * r ** 2, m / 4 * r ** 2)
BodyD = RigidBody("BodyD", Dmc, R, m, (I, Dmc))
BodyD.potential_energy = -m * g * r * cos(q2)
Lag = Lagrangian(N, BodyD)
l = LagrangesMethod(Lag, q)
l.form_lagranges_equations()
# Linearize about steady-state upright rolling
op_point = {q1: 0, q2: 0, q3: 0, q1d: 0, q2d: 0, q1d.diff(): 0, q2d.diff(): 0, q3d.diff(): 0}
A = l.linearize(q_ind=q, qd_ind=qd, op_point=op_point, A_and_B=True)[0]
sol = Matrix(
[
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, -6 * q3d, 0],
[0, -4 * g / (5 * r), 0, 6 * q3d / 5, 0, 0],
[0, 0, 0, 0, 0, 0],
]
)
assert A == sol
示例15: Point
pC_star = Point('pC*') # center of mass of rod
pA_star = pC_star.locatenew('pA*', L/2*C.x) # center of disk A
pB_star = pC_star.locatenew('pB*', -L/2*C.x) # center of disk A
pA_hat = pA_star.locatenew('pA^', -r*C.z) # contact point of disk A and ground
pB_hat = pB_star.locatenew('pB^', -r*C.z) # contact point of disk A and ground
pC_star.set_vel(N, v*C.y)
pA_star.v2pt_theory(pC_star, N, C) # pA* and pC* are both fixed in frame C
pB_star.v2pt_theory(pC_star, N, C) # pB* and pC* are both fixed in frame C
pA_hat.v2pt_theory(pA_star, N, A) # pA* and pA^ are both fixed in frame A
pB_hat.v2pt_theory(pB_star, N, B) # pB* and pB^ are both fixed in frame B
I_rod = inertia(C, 0, m0*L**2/12, m0*L**2/12, 0, 0, 0)
rbC = RigidBody('rod_C', pC_star, C, m0, (I_rod, pC_star))
I_discA = inertia(A, m*r**2/2, m*r**2/4, m*r**2/4, 0, 0, 0)
rbA = RigidBody('disc_A', pA_star, A, m, (I_discA, pA_star))
I_discB = inertia(B, m*r**2/2, m*r**2/4, m*r**2/4, 0, 0, 0)
rbB = RigidBody('disc_B', pB_star, B, m, (I_discB, pB_star))
print('omega_A_N = {}'.format(msprint(A.ang_vel_in(N).express(C))))
print('v_pA*_N = {}'.format(msprint(pA_hat.vel(N))))
qd_val = solve([dot(pA_hat.vel(N), C.y), dot(pB_hat.vel(N), C.y)],
[q2d, q3d])
print(msprint(qd_val))
print('T_A = {}'.format(msprint(simplify(rbA.kinetic_energy(N).subs(qd_val)))))