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Fixed the update rule, except for friction (sort of). Set c1/c2 to 0. #1

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Fixed the update rule, except for friction (sort of). Set c1/c2 to 0. #1

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94 changes: 75 additions & 19 deletions main.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,7 @@

import numpy as np
from abc import ABCMeta, abstractmethod
import matplotlib.pyplot as plt


def normalize_angle(angle):
Expand All @@ -25,14 +26,18 @@ def step_until(self, time):

class DoublePendulumSimulation(Simulation):

def __init__(self, dt, g, m1, m2, l1, l2, t, theta1, theta2, omega1=0, omega2=0, alpha1=0, alpha2=0, use_angle_normalization=False):
def __init__(self, dt, g, m1, m2, l1, l2, I1, I2, c1, c2, t, theta1, theta2, omega1=0, omega2=0, alpha1=0, alpha2=0, use_angle_normalization=False):
# Constants
self.dt = dt
self.g = g
self.m1 = m1
self.m2 = m2
self.l1 = l1
self.l2 = l2
self.I1 = I1
self.I2 = I2
self.c1 = c1
self.c2 = c2

# Variables
self.t = t
Expand All @@ -57,6 +62,10 @@ def do_step(self):
m2 = self.m2
l1 = self.l1
l2 = self.l2
I1 = self.I1
I2 = self.I2
c1 = self.c1
c2 = self.c2

# Variables
t = self.t
Expand All @@ -76,22 +85,46 @@ def do_step(self):
self.omega1 = omega1 + alpha1 * dt
self.omega2 = omega2 + alpha2 * dt

self.alpha1 = (
- g * (2 * m1 + m2) * np.sin(theta1)
- m2 * g * np.sin(theta1 - 2 * theta2)
- 2 * np.sin(theta1 - theta2) * m2 * (
+ omega2 ** 2 * l2
+ omega1 ** 2 * l1 * np.cos(theta1 - theta2)
)
) / (l1 * (2 * m1 + m2 - m2 * np.cos(2 * theta1 - 2 * theta2)))

self.alpha2 = (
2 * np.sin(theta1 - theta2) * (
+ omega1 ** 2 * l1 * (m1 + m2)
+ g * (m1 + m2) * np.cos(theta1)
+ omega2 ** 2 * l2 * m2 * np.cos(theta1 - theta2)
)
) / (l2 * (2 * m1 + m2 - m2 * np.cos(2 * theta1 - 2 * theta2)))
# self.alpha1 = (
# - g * (2 * m1 + m2) * np.sin(theta1)
# - m2 * g * np.sin(theta1 - 2 * theta2)
# - 2 * np.sin(theta1 - theta2) * m2 * (
# + omega2 ** 2 * l2
# + omega1 ** 2 * l1 * np.cos(theta1 - theta2)
# )
# ) / (l1 * (2 * m1 + m2 - m2 * np.cos(2 * theta1 - 2 * theta2)))

# self.alpha2 = (
# 2 * np.sin(theta1 - theta2) * (
# + omega1 ** 2 * l1 * (m1 + m2)
# + g * (m1 + m2) * np.cos(theta1)
# + omega2 ** 2 * l2 * m2 * np.cos(theta1 - theta2)
# )
# ) / (l2 * (2 * m1 + m2 - m2 * np.cos(2 * theta1 - 2 * theta2)))

I1_ = m1*l1**2 / 4 + m2*l1**2 + I1
I2_ = m2*l2**2 / 4 + m2*l2**2 + I2
k = m2*l1*l2 / 2
A = (m1 + 2*m2)/2*g*l1
B = 1/2*m2*g*l2
Fw1 = c1*omega1**2*l1**2 / I1_ * (omega1 > 0) - c1*omega1**2*l1**2 / I1_ * (omega2 <= 0)
Fw2 = c2*((omega1*l1*np.cos(theta1) + omega2*l2*np.cos(theta2))**2 +
(omega1*l1*np.sin(theta1) + omega2*l2*np.sin(theta2))**2) * (omega2 > 0) - \
c2*((omega1*l1*np.cos(theta1) + omega2*l2*np.cos(theta2))**2 +
(omega1*l1*np.sin(theta1) + omega2*l2*np.sin(theta2))**2) * (omega2 <= 0)

self.alpha1 = - (k*omega2**2 * np.sin(theta1 - theta2) + k*alpha2*np.cos(theta1 - theta2) + A*np.sin(theta1) + Fw1) / I1
self.alpha2 = (k*omega1**2 * np.sin(theta1 - theta2) - k*alpha1*np.cos(theta1 - theta2) - B*np.sin(theta2) + \
k*omega1**2 * np.sin(theta1 - theta2) - k*alpha1*np.cos(theta1 - theta2) - B*np.sin(theta2) - Fw2) / I2_

# self.alpha1 = - (m2*alpha2*l1*l2*np.cos(theta1-theta2) \
# + 1/2*m2*omega2**2*l1*l2*np.sin(theta1-theta2) \
# + (m1+2*m2)/2*g*l1*np.sin(theta1)) \
# / (1/4*m1*l1**2+m2*l1**2+I1)
# self.alpha2 = (-1/2*m2*alpha2*l1*l2*np.cos(theta1-theta2) \
# + 1/2*m2*omega1**2*l1*l2*np.sin(theta1-theta2) \
# - m2/2*g*l2*np.sin(theta2)) \
# / (1/4*m2*l2**2 + I2)

def simplify_theta(self, theta):
if self.use_angle_normalization:
Expand All @@ -113,9 +146,13 @@ def simplify_theta(self, theta):
m2=1,
l1=np.full(10, 1),
l2=np.full(10, 1),
I1=1,
I2=1,
c1=1,
c2=1,
t=0,
theta1=np.full(10, np.pi),
theta2=np.linspace(np.pi * 0.99990, np.pi - 0.00001, 10),
theta1=-np.full(10, np.pi),
theta2=np.linspace(np.pi * 0.9990, np.pi - 0.0001, 10),
)

### Simulation
Expand All @@ -136,6 +173,12 @@ def simplify_theta(self, theta):

time_start = None

# PLOTTING
prev_sim_time = 0
ts = []
y1s = []
y2s = []

run_simulation = False
while True:
surface.fill((255, 255, 255))
Expand Down Expand Up @@ -178,6 +221,19 @@ def simplify_theta(self, theta):
elif event.key == pygame.K_MINUS:
time_scale = time_scale / 1.1

if sim.get_time() - prev_sim_time > 0:
print(sim.get_time())
ts += [sim.get_time()]
y1s += [np.std(theta1_array)]
y2s += [np.std(theta2_array)]
prev_sim_time += .1
if sim.get_time() > 45:
break

plt.plot(ts, y1s)
plt.plot(ts, y2s)
plt.show()

# stop_t = 10
#
# anim_time = 0
Expand Down