# Import Libraries: import numpy as np import matplotlib.pyplot as plt import sympy as sp from matplotlib.animation import FFMpegWriter from matplotlib.patches import Circle !apt update -y !apt install ffmpeg -y # Parameters g = 9.81 # m/s2 m = 1 # kg dt = 0.001 t_vec = np.arange(0,10,dt) # Zero Vectors x_vec = np.zeros(len(t_vec)) dx_vec = np.zeros(len(t_vec)) ddx_vec = np.zeros(len(t_vec)) y_vec = np.zeros(len(t_vec)) dy_vec = np.zeros(len(t_vec)) ddy_vec = np.zeros(len(t_vec)) lamda_vec = np.zeros(len(t_vec)) # Initial Conditions x_vec[0] = -1 # x position y_vec[0] = 1 # y position dx_vec[0] = 0 # x velocity dy_vec[0] = 0 # y velocity # Euler's Method for i in range(1, len(t_vec)): # X x_vec[i] = x_vec[i-1] + dx_vec[i-1]*dt ddx_vec[i-1] = -(x_vec[i-1]*(200*(dx_vec[i-1]**2) + 981))/(50*(4*(x_vec[i-1]**2) + 1)) dx_vec[i] = dx_vec[i-1] + ddx_vec[i-1]*dt # Y y_vec[i] = x_vec[i]**2 # Constraints lamda_vec[i] = (2*m*dx_vec[i-1]**2 + g*m)/(4*dx_vec[i-1]**2 + 1) # X Position Plot figure1= plt.plot(t_vec, x_vec) plt.title('MOD HW 1B: X Position') plt.show() # Y Position Plot figure2 = plt.plot(t_vec, y_vec) plt.title('MOD HW 1B: Y Position') plt.show() # Constraints figure3 = plt.plot(t_vec, lamda_vec) plt.title('Homework 1B: Constraints') plt.show() # Initialize Figure and Axes fig, ax = plt.subplots() p, = ax.plot([], [], color='blue') ax.axis('equal') ax.set_xlim([-3, 3]) ax.set_ylim([-3, 3]) # Labels ax.set_xlabel('X') ax.set_ylabel('Y') # Title ax.set_title('MOD Simulation 1C:') video_title = "MOD Simulation 1C" # name of the mp4 # Initialize Patch c = Circle((-1, 1), radius=0.1, color='red') ax.add_patch(c) # Add the patch to the axes # Setup Animation Writer FPS = 20 # Frames per second for the video sample_rate = int(1 / (dt * FPS)) # Rate at which we sample the simulation to visualize dpi = 300 # Quality of the Video writerObj = FFMpegWriter(fps=FPS) # Video Object x_func = np.linspace(-2, 2, 2000) y_func = x_func**2 fig3 = plt.plot(x_func, y_func) plt.xlim([-2, 2]) plt.ylim([-0.5, 2.5]) plt.show() simulation_size = len(t_vec) with writerObj.saving(fig, video_title+".mp4", dpi): for i in range(0, simulation_size, sample_rate): p.set_data(x_vec[i], y_vec[i]) patch_center = x_vec[i], y_vec[i] c.center = patch_center fig.canvas.draw() writerObj.grab_frame() from IPython.display import Video Video("/work/MOD Simulation 1C.mp4",embed=True, width=640,height=480)