Математический маятник

import numpy as np
import matplotlib.pyplot as plt
from math import *
 
 
get_ipython().run_line_magic('matplotlib', 'inline')
get_ipython().run_line_magic('matplotlib', 'notebook')
 
fig, ax = plt.subplots(figsize=(10, 5), dpi=80)
plt.subplots_adjust(left=0.3, bottom=0.3)
 
 
class solution(object):
    def __init__(self, omega_0 = 0, theta_0 = 10, eta=0.01, n_iter=10):
        self.omega_0 = omega_0
        self.theta_0 = theta_0
        self.eta = eta
        self.n_iter = n_iter
    
    def euler(self,alpha):
        self.time_ = np.zeros(self.n_iter)
        self.omega_ = np.zeros(self.n_iter)
        self.theta_ = np.zeros(self.n_iter)
        self.omega_[0] = self.omega_0
        self.theta_[0] = self.theta_0*np.pi/180.0
        
        for i in range(self.n_iter-1):
            self.time_[i+1] = self.time_[i] + self.eta
            self.omega_[i+1] = self.omega_[i] + self.eta*alpha(self.theta_[i])
            self.theta_[i+1] = self.theta_[i] + self.eta*self.omega_[i]
        return self
    
    def midpoint(self,alpha):
        self.time_ = np.zeros(self.n_iter)
        self.omega_ = np.zeros(self.n_iter)
        self.theta_ = np.zeros(self.n_iter)
        self.omega_[0] = self.omega_0
        self.theta_[0] = self.theta_0*np.pi/180.0
        
        for i in range(self.n_iter-1):
            self.time_[i+1] = self.time_[i] + self.eta
            self.omega_[i+1] = self.omega_[i] + self.eta*alpha(self.theta_[i])
            self.theta_[i+1] = self.theta_[i] + 0.5*self.eta*(self.omega_[i]+self.omega_[i+1])
        return self
 
    
def alpha(x):
    return -np.sin(x)