"""
This file will use pydy.codegen to simulate the double pendulum.
"""
from numpy import concatenate, array, linspace
from pydy.system import System
from scipy.integrate import odeint
from double_pendulum import *
constants = {l: 10.0, m: 10.0, g: 9.81}
initial_conditions = {q1: 1.0, q2: 0.0, u1: 0.0, u2: 0.0}
sys = System(KM, constants=constants,
initial_conditions=initial_conditions)
frames_per_sec = 60
final_time = 5.0
times = linspace(0.0, final_time, final_time * frames_per_sec)
sys.times = times
x = sys.integrate()
Ir: rod_inertia,
L1: Length1_values[i],
L2: Length2_values[i],
e_offset: e_offset_scalar,
k_C: spring_on_frame_C
}
sys.initial_conditions = {
x: x_values_heat_np[i],
z: z_values_heat_np[i],
theta: theta_values_heat_np[i, 0],
e: e_equil,
phi: theta_values_heat_np[i, 0]
}
sys.times = np.linspace(0.0, runtime, runtime * 30)
sys.generate_ode_function(generator='cython')
resp = sys.integrate()
true_x_pre.append(resp[:, 0][-1])
true_z_pre.append(resp[:, 1][-1])
true_e_pre.append(resp[:, 2][-1])
true_theta_pre.append(resp[:, 3][-1])
true_phi_pre.append(resp[:, 4][-1])
print(i)
true_x = np.asarray(true_x_pre)
true_z = np.asarray(true_z_pre)
true_e = np.asarray(true_e_pre)
true_theta = np.asarray(true_theta_pre)
true_phi = np.asarray(true_phi_pre)
np.save('true_x', true_x)
np.save('true_z', true_z)
np.save('true_e', true_e)
def example_pydy(ax=None, **options):
"""
Example from the documentation of
:epkg:`pydy`.
@param ax matplotlib axis
@parm options extra options
@return ax
"""
# part 1
from sympy import symbols
import sympy.physics.mechanics as me
mass, stiffness, damping, gravity = symbols('m, k, c, g')
position, speed = me.dynamicsymbols('x v')
positiond = me.dynamicsymbols('x', 1)
force = me.dynamicsymbols('F')
ceiling = me.ReferenceFrame('N')
origin = me.Point('origin')
origin.set_vel(ceiling, 0)
center = origin.locatenew('center', position * ceiling.x)
center.set_vel(ceiling, speed * ceiling.x)
block = me.Particle('block', center, mass)
kinematic_equations = [speed - positiond]
force_magnitude = mass * gravity - stiffness * position - damping * speed + force
forces = [(center, force_magnitude * ceiling.x)]
particles = [block]
kane = me.KanesMethod(ceiling,
q_ind=[position],
u_ind=[speed],
kd_eqs=kinematic_equations)
kane.kanes_equations(forces, particles)
# part 2
from numpy import linspace, sin
from pydy.system import System
sys = System(kane,
constants={
mass: 1.0,
stiffness: 1.0,
damping: 0.2,
gravity: 9.8
},
specifieds={
force: lambda x, t: sin(t)
},
initial_conditions={
position: 0.1,
speed: -1.0
},
times=linspace(0.0, 10.0, 1000))
y = sys.integrate()
# part 3
import matplotlib.pyplot as plt
if ax is None:
_, ax = plt.subplots(nrows=1,
ncols=1,
figsize=options.get('figsize', (5, 5)))
ax.plot(sys.times, y)
ax.legend((str(position), str(speed)))
return ax
def example_pydy(ax=None, **options):
"""
Example from the documentation of
:epkg:`pydy`.
@param ax matplotlib axis
@parm options extra options
@return ax
"""
# part 1
from sympy import symbols
import sympy.physics.mechanics as me
mass, stiffness, damping, gravity = symbols('m, k, c, g')
position, speed = me.dynamicsymbols('x v')
positiond = me.dynamicsymbols('x', 1)
force = me.dynamicsymbols('F')
ceiling = me.ReferenceFrame('N')
origin = me.Point('origin')
origin.set_vel(ceiling, 0)
center = origin.locatenew('center', position * ceiling.x)
center.set_vel(ceiling, speed * ceiling.x)
block = me.Particle('block', center, mass)
kinematic_equations = [speed - positiond]
force_magnitude = mass * gravity - stiffness * position - damping * speed + force
forces = [(center, force_magnitude * ceiling.x)]
particles = [block]
kane = me.KanesMethod(ceiling, q_ind=[position], u_ind=[speed],
kd_eqs=kinematic_equations)
kane.kanes_equations(forces, particles)
# part 2
from numpy import linspace, sin
from pydy.system import System
sys = System(kane,
constants={mass: 1.0, stiffness: 1.0,
damping: 0.2, gravity: 9.8},
specifieds={force: lambda x, t: sin(t)},
initial_conditions={position: 0.1, speed: -1.0},
times=linspace(0.0, 10.0, 1000))
y = sys.integrate()
# part 3
import matplotlib.pyplot as plt
if ax is None:
_, ax = plt.subplots(
nrows=1, ncols=1, figsize=options.get('figsize', (5, 5)))
ax.plot(sys.times, y)
ax.legend((str(position), str(speed)))
return ax
