CoCalc Public Filestest-zhidkov.ipynb
Author: Evgenij Grines
Views : 78
Description: Jupyter notebook test-zhidkov.ipynb
Compute Environment: Ubuntu 18.04 (Deprecated)
In [1]:
from numpy import sin, cos
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as integrate
from ipywidgets import *

In [2]:
G = 9.8  # acceleration due to gravity, in m/s^2

def derivs(state, t,params):
L1, L2, M1, M2 = params

dydx = np.zeros_like(state)
dydx[0] = state[1]

del_ = state[2] - state[0]
den1 = (M1 + M2)*L1 - M2*L1*cos(del_)*cos(del_)
dydx[1] = (M2*L1*state[1]*state[1]*sin(del_)*cos(del_) +
M2*G*sin(state[2])*cos(del_) +
M2*L2*state[3]*state[3]*sin(del_) -
(M1 + M2)*G*sin(state[0]))/den1

dydx[2] = state[3]

den2 = (L2/L1)*den1
dydx[3] = (-M2*L2*state[3]*state[3]*sin(del_)*cos(del_) +
(M1 + M2)*G*sin(state[0])*cos(del_) -
(M1 + M2)*L1*state[1]*state[1]*sin(del_) -
(M1 + M2)*G*sin(state[2]))/den2

return dydx

In [3]:
def example(th1,w1,th2,w2,l1,l2,m1,m2, Tmax):
pars = (l1, l2, m1, m2)
ders = lambda state, t: derivs(state, t, pars)
dt = 0.001
t = np.arange(0.0, Tmax, dt)
state = np.radians([th1, w1, th2, w2])
y = integrate.odeint(ders, state, t)
x1 = l1*sin(y[:, 0])
y1 = -l1*cos(y[:, 0])
x2 = l2*sin(y[:, 2]) + x1
y2 = -l2*cos(y[:, 2]) + y1
plt.plot(x2,y2, label = 'bottom pendulum')
plt.legend()
plt.scatter([0.0],[0.0],c='orange',s=36.0)
plt.scatter([x2[0]],[y2[0]],c='green',s=36.0)
plt.scatter([x2[-1]],[y2[-1]],c='red',s=36.0)

In [4]:
interact(example,
th1 = BoundedFloatText(value=120.0, min = - 180.0, max = 180.0, description='Angle 1 (degrees):'),
w1 = FloatText(value=0.0, description='Angular velocity 1:'),
th2 = BoundedFloatText(value=-10.0, min = - 180.0, max = 180.0, description='Angle 2 (degrees):'),
w2 = FloatText(value=0.0, description='Angular velocity 2:'),
l1 = BoundedFloatText(value=1.0, min = 0.01, max = 5.0, description='L1:'),
l2 = BoundedFloatText(value=1.0, min = 0.01, max = 5.0, description='L2:'),
m1 = BoundedFloatText(value=1.0, min = 0.01, max = 10.0, description='M1:'),
m2 = BoundedFloatText(value=1.0, min = 0.01, max = 10.0, description='M2:'),
Tmax = BoundedFloatText(value=20.0, min = 0.01, max = 1000.0, description='Max time:'),
__manual=True)

<function __main__.example>
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