MOD_Homework1_Q2

!apt update -y !apt install ffmpeg -y import numpy as np import matplotlib.pyplot as plt from matplotlib.animation import FFMpegWriter from matplotlib.patches import Circle # Defining our Parameters g = 9.8 # Gravity (m/s^2) L = 1 # Length (m) m_1 = 1 # In Kg m_2 = 2 # In Kg k = 10 # Spring Constant (N/m) h = 1.5 # Height of Hinge from ground (m) # Creating the time array for 10 second run time dt = 0.001 # Seconds (s) t_vec = np.arange(0,10,dt) # Time Vector # Define vectors that will hold our state variables over time # x Vectors of Zero x_vec = np.zeros(len(t_vec)) dx_vec = np.zeros(len(t_vec)) ddx_vec = np.zeros(len(t_vec)) # theta Vectors of Zero theta_vec = np.zeros(len(t_vec)) dtheta_vec = np.zeros(len(t_vec)) ddtheta_vec = np.zeros(len(t_vec)) # Vector for hinge location y = np.zeros(len(t_vec)) # Establishing the initial conditions for x & theta x_vec[0] = 0 # x Initial Position dx_vec[0] = 0 # dx Initial Velocity theta_vec[0] = 1 # theta Initial Position dtheta_vec[0] = 0 # dtheta Initial Velocity # Loop through time # Creating Loop to run through the theta direction # The Code works once you remove "...", I could not figure out text wrapping 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]))))/(m_1*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 # Creating Loop to run through the x direction for i in range(1, len(t_vec)): x_vec[i] = x_vec[i-1] + dx_vec[i-1]*dt # The Code works once you remove "...", I could not figure out text wrapping 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]))/(m_2*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 # Setting up for the x component on graph plt.plot(t_vec, x_vec) plt.title('X - component') plt.show() # Setting up for the y component on graph plt.plot(t_vec, theta_vec) plt.title('Theta - component') plt.show() # SETTING UP THE SIMULATION # Setup Figure: Initialize Figure / Axe Handles fig, ax = plt.subplots() # Initialize Figure and Axis p1, = ax.plot([], [], color='dodgerblue') # Initialize Empty Plot p2, = ax.plot([], [], color='dodgerblue') # Initialize Empty Plot ax.axis('equal') # Setting Parameters for plot ax.set_xlim([-3, 3]) ax.set_ylim([-3, 3]) # Setting up labels for plot ax.set_xlabel('X') # X Label ax.set_ylabel('Y') # Y Label ax.set_title('Pendulum Simulation:') video_title = "simulation 2C" # Naming Of Animation # Initialize Patch: (Circle From Pendelum) # Draws a circle of on the plot at the origin c = Circle((0, -0.75), radius=0.1, color='dodgerblue') ax.add_patch(c) # Adds Patch to PLot # Initialize Patch: (Rectangle on Ground) # Couldnt get right positioning so used a circle instead #width = .5 # Width of rectangle #height = .3 # Hieght of rectangle #xy_rec = (x_vec[0]+ width, -h + height) #b = Rectangle(xy_rec, width,height, color='mediumseagreen') #ax.add_patch(b) # Adds Patch to PLot # Implemented circle to show movements b = Circle((0, -1.5), radius=0.2, color='dodgerblue') ax.add_patch(b) # Setup Animation Writer: FPS = 20 # Frames per second for the video # Rate at which we sample the simulation to visualize sample_rate = int(1 / (dt * FPS)) dpi = 300 # Quality of the Video writerObj = FFMpegWriter(fps=FPS) # Video Object # We need to calculate the cartesian location of the pendulum: # Initialize Array: 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 # Find the X and Y trajectories of the 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]] # We want to avoid creating new plots to make an animation (Very Slow) # Instead lets take the plot we made earlier and just update it with new data. p1.set_data(x_data_points, y_data_points) # Update plot with set_data p2.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 # Update Drawing: fig.canvas.draw() # Update the figure with the new changes # Grab and Save Frame: writerObj.grab_frame() # We can also run it inline with the following block of code: from IPython.display import Video Video("/work/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"