我正在使用SymPy力学模块生成三重摆系统的动画。在使用Kane方法的模型构建阶段，粒子列表开始时是一个空列表，然后添加粒子计算。在调用kanes_equations中的粒子列表时，我遇到了"不能解包不可迭代的粒子对象"，尽管力列表经过相同的过程并且没有抛出错误。
def integrate_pendulum(n, times,
initial_positions=135,
initial_velocities=0,
lengths=None, masses=1):
"""Integrate a multi-pendulum with `n` sections"""
#-------------------------------------------------
# Step 1: construct the pendulum model
# Generalized coordinates and velocities
# (in this case, angular positions & velocities of each mass)
q = mechanics.dynamicsymbols('q:{0}'.format(n))
u = mechanics.dynamicsymbols('u:{0}'.format(n))
# mass and length
m = symbols('m:{0}'.format(n))
l = symbols('l:{0}'.format(n))
# gravity and time symbols
g, t = symbols('g,t')
#--------------------------------------------------
# Step 2: build the model using Kane's Method
# Create pivot point reference frame
A = mechanics.ReferenceFrame('A')
P = mechanics.Point('P')
P.set_vel(A, 0)
# lists to hold particles, forces, and kinetic ODEs
# for each pendulum in the chain
particles = []
forces = []
kinetic_odes = []
for i in range(n):
# Create a reference frame following the i^th mass
Ai = A.orientnew('A' + str(i), 'Axis', [q[i], A.z])
Ai.set_ang_vel(A, u[i] * A.z)
# Create a point in this reference frame
Pi = P.locatenew('P' + str(i), l[i] * Ai.x)
Pi.v2pt_theory(P, A, Ai)
# Create a new particle of mass m[i] at this point
# Pai = mechanics.Particle('Pa' + str(i), Pi, m[i])
Pai = mechanics.Particle('Pa' + str(i), Pi, m[i])
particles.append(Pai)
# Set forces & compute kinematic ODE
forces.append((Pi, m[i] * g * A.x))
kinetic_odes.append(q[i].diff(t) - u[i])
P = Pi
# Generate equations of motion
KM = mechanics.KanesMethod(A, q_ind=q, u_ind=u,
kd_eqs=kinetic_odes)
fr, fr_star = KM.kanes_equations(forces, particles)
#-----------------------------------------------------
# Step 3: numerically evaluate equations and integrate
# initial positions and velocities – assumed to be given in degrees
y0 = np.deg2rad(np.concatenate([np.broadcast_to(initial_positions, n),
np.broadcast_to(initial_velocities, n)]))
# lengths and masses
if lengths is None:
lengths = np.ones(n) / n
lengths = np.broadcast_to(lengths, n)
masses = np.broadcast_to(masses, n)
# Fixed parameters: gravitational constant, lengths, and masses
parameters = [g] + list(l) + list(m)
parameter_vals = [9.81] + list(lengths) + list(masses)
# define symbols for unknown parameters
unknowns = [Dummy() for i in q + u]
unknown_dict = dict(zip(q + u, unknowns))
kds = KM.kindiffdict()
# substitute unknown symbols for qdot terms
mm_sym = KM.mass_matrix_full.subs(kds).subs(unknown_dict)
fo_sym = KM.forcing_full.subs(kds).subs(unknown_dict)
# create functions for numerical calculation
mm_func = lambdify(unknowns + parameters, mm_sym)
fo_func = lambdify(unknowns + parameters, fo_sym)
# function which computes the derivatives of parameters
def gradient(y, t, args):
vals = np.concatenate((y, args))
sol = np.linalg.solve(mm_func(*vals), fo_func(*vals))
return np.array(sol).T[0]
# ODE integration
return odeint(gradient, y0, times, args=(parameter_vals,))
我正在运行以下代码来尝试生成显示钟摆运动历史的绘图
t = np.linspace(0, 10, 1000)
p = integrate_pendulum(n=3, times=t)
x, y = get_xy_coords(p)
plt.plot(x, y);
我期望看到一个类似于下面的情节:三摆运动历史
但是代码似乎无法以当前保存的形式解包粒子函数。我不太熟悉这个代码，因为它不是我的，我希望修改它为我的需要。
kanes_equations()在几年前被弃用了。API现在是:
fr, frstar = kane。kanes_equations(粒子,部队)
与原文代码中看到的(力，粒子)相反。