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.
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Question
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa98117fc-4537-4efb-9016-9993926a8208%2F36e6c536-154b-4e65-9a5e-c3b863e5facd%2F8ug6c1m_processed.png&w=3840&q=75)
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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Follow-up Questions
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Follow-up Question
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()](https://content.bartleby.com/qna-images/question/a98117fc-4537-4efb-9016-9993926a8208/81fad2ad-d008-47a9-842e-a33d477b6b7a/tgybfni_thumbnail.png)
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()
Solution
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