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A plane is heading to LAX with constant acceleration of 60 km/h². At time t = 0, the plane stays still at position 0 km. The state of the plane is measured every hour. (In other words, there is an hour between t and t + 1). The state vector x has 3 components. x = x1 X2 X3 position velocity [acceleration] For motion with constant acceleration, the velocity v of the object at time t2 is calculated using equation Vt₂ = Vt₁ + a(t2 − t₁). The position a of the object at time tą is calculated using equation æ₁₂ = x₁, +v₁₂(t2 − t₁) + ½ a(t2 − t₁)². 1 (a) Model the problem as a linear dynamical system.

A plane is heading to LAX with constant acceleration of 60 km/h². At time t = 0, the plane stays still at position 0 km. The state of the plane is measured every hour. (In other words, there is an hour between t and t + 1). The state vector x has 3 components. x = x1 X2 X3 position velocity [acceleration] For motion with constant acceleration, the velocity v of the object at time t2 is calculated using equation Vt₂ = Vt₁ + a(t2 − t₁). The position a of the object at time tą is calculated using equation æ₁₂ = x₁, +v₁₂(t2 − t₁) + ½ a(t2 − t₁)². 1 (a) Model the problem as a linear dynamical system.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Linear Dynamical system help, PLS more detals and clearly to see.

A plane is heading to LAX with constant acceleration of 60 km/h². At time t = 0, the plane stays still at position 0 km. The state of the plane is measured every hour. (In other words, there is an hour between t and t + 1). The state vector x has 3 components. x = x1 X2 x3 = position velocity Lacceleration_ = For motion with constant acceleration, the velocity v of the object at time tê is calculated using equation V2 The position of the object at time t2 is calculated using equation ₂ = xt₁ + vt₁(t2 − t₁) + = a(t2 − t₁)² . (a) Model the problem as a linear dynamical system. (b) Use python to simulate the state vector for 10 hours. vt₁ + a(t2 − t₁).
Transcribed Image Text:A plane is heading to LAX with constant acceleration of 60 km/h². At time t = 0, the plane stays still at position 0 km. The state of the plane is measured every hour. (In other words, there is an hour between t and t + 1). The state vector x has 3 components. x = x1 X2 x3 = position velocity Lacceleration_ = For motion with constant acceleration, the velocity v of the object at time tê is calculated using equation V2 The position of the object at time t2 is calculated using equation ₂ = xt₁ + vt₁(t2 − t₁) + = a(t2 − t₁)² . (a) Model the problem as a linear dynamical system. (b) Use python to simulate the state vector for 10 hours. vt₁ + a(t2 − t₁).
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I'm still comfusion about Part A. Can you explain it more Clearly? 

And also, I got the sample code for part B, Can you modify the code base on it?

import matplotlib.pyplot as plt import numpy as np X0 = A = states = np.zeros((11,3)) states [0] = x0 # Use for loop to calculate x_t for t in range (1,11): # Plotting times = np.arange(0, 11, 1) plt.plot(times, plt.plot(times, plt.plot(times, • • • / # Adding legend plt.legend() color='r', label='Plane Position') color='g', label='Plane Velocity') color='b', label='Plane Acceleration') # Naming the x-axis, y-axis and the whole graph plt.xlabel("Time" plt.ylabel("State Vector") plt.title("State Trajectory of the Plane") # To load the display window plt.show()
Transcribed Image Text:import matplotlib.pyplot as plt import numpy as np X0 = A = states = np.zeros((11,3)) states [0] = x0 # Use for loop to calculate x_t for t in range (1,11): # Plotting times = np.arange(0, 11, 1) plt.plot(times, plt.plot(times, plt.plot(times, • • • / # Adding legend plt.legend() color='r', label='Plane Position') color='g', label='Plane Velocity') color='b', label='Plane Acceleration') # Naming the x-axis, y-axis and the whole graph plt.xlabel("Time" plt.ylabel("State Vector") plt.title("State Trajectory of the Plane") # To load the display window plt.show()
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