# Import Libraries: import numpy as np import matplotlib.pyplot as plt from matplotlib.animation import FFMpegWriter from matplotlib.patches import Circle !apt update -y !apt install ffmpeg -y # Parameters g = 9.8 # m/s2 m1 = 1 # kg m2 = 2 # kg L = 1 # m k = 10 # N/m h = 1.5 #m 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)) theta_vec = np.zeros(len(t_vec)) dtheta_vec = np.zeros(len(t_vec)) ddtheta_vec = np.zeros(len(t_vec)) y = np.zeros(len(t_vec)) # Initial Conditions x_vec[0] = 0 # x position theta_vec[0] = 1 # y position dx_vec[0] = 0 # x velocity dtheta_vec[0] = 0 # y velocity # Eulers Method for i in range(1, len(t_vec)): theta_vec[i] = theta_vec[i-1] + dtheta_vec[i-1]*dt ddtheta_vec[i-1] = -((g*np.sin(theta_vec[i-1]))/(L)) - (k*(np.sqrt((L*np.sin(theta_vec[i-1]) - x_vec[i-1])**2 + (h - L*np.cos(theta_vec[i-1]))**2) - L)*((L*np.sin(theta_vec[i-1]) - x_vec[i-1])*(L*np.cos(theta_vec[i-1])) + (h - L*np.cos(theta_vec[i-1]))*(L*np.sin(theta_vec[i-1]))))/ (m1*L**2*np.sqrt((L*np.sin(theta_vec[i-1]) - x_vec[i-1])**2 + (h - L*np.cos(theta_vec[i-1]))**2)) dtheta_vec[i] = dtheta_vec[i-1] + ddtheta_vec[i-1]*dt x_vec[i] = x_vec[i-1] + dx_vec[i-1]*dt ddx_vec[i-1] = (k*(np.sqrt((L*np.sin(theta_vec[i-1]) - x_vec[i-1])**2 + (h - L*np.cos(theta_vec[i-1]))**2) - L)*(L*np.sin(theta_vec[i-1]) - x_vec[i-1]))/(m2*np.sqrt((L*np.sin(theta_vec[i-1]) - x_vec[i-1])**2 + (h - L*np.cos(theta_vec[i-1]))**2)) dx_vec[i] = dx_vec[i-1] + ddx_vec[i-1]*dt y[i] = -1.5 # X Position Plot plt.plot(t_vec, x_vec) plt.title('MOD HW 2B: X Position') plt.show() # Theta Plot plt.plot(t_vec, theta_vec) plt.title('MOD HW 2B: Theta') plt.show() # Initialize Figure and Axes fig, ax = plt.subplots() # Initialize Empty Plot p, = ax.plot([], [], color='black') q, = ax.plot([], [], color='black') ax.axis('equal') ax.set_xlim([-3, 3]) ax.set_ylim([-3, 3]) # Labels ax.set_xlabel('X') ax.set_ylabel('Y') ax.set_title('MOD Simulation 2C:') # Plot Title video_title = "MOD Simulation 2C" # name of the mp4 # Initialize Patch c = Circle((0, -0.65), radius=0.2, color='red') ax.add_patch(c) # Add the patch to the axes b = Circle((0, -1.5), radius=0.2, color='blue') ax.add_patch(b) # 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 # Cartesian location of pendulum simulation_size = len(t_vec) # We use this alot, so lets store it. x_pendulum_arm = np.zeros(simulation_size) y_pendulum_arm = np.zeros(simulation_size) origin = (0, 0) # Pin Joint (X, Y) Location # Trajectories of pendulum for i in range(0, simulation_size): x_pendulum_arm[i] = L * np.sin(theta_vec[i]) + origin[0] y_pendulum_arm[i] = origin[1] - L * np.cos(theta_vec[i]) # Plot and Create Animation with writerObj.saving(fig, video_title+".mp4", dpi): # We want to create video that represents the simulation # So we need to sample only a few of the frames: for i in range(0, simulation_size, sample_rate): # Update Pendulum Arm x_data_points = [origin[0], x_pendulum_arm[i]] y_data_points = [origin[1], y_pendulum_arm[i]] x2_data_points = [x_vec[i], x_pendulum_arm[i]] y2_data_points = [y[i], y_pendulum_arm[i]] p.set_data(x_data_points, y_data_points) # Update plot q.set_data(x2_data_points, y2_data_points) # Update Pendulum Patch: patch_center = x_pendulum_arm[i], y_pendulum_arm[i] c.center = patch_center m_center = x_vec[i], y[i] b.center = m_center fig.canvas.draw() # Grab and Save Frame: writerObj.grab_frame() from IPython.display import Video Video("/work/MOD Simulation 2C.mp4", embed=True, width=640, height=480) # You can find the video's path by right clicking on it in Notebooks & Files # and selecting "Copy path to clipboard"