7-5. Consider a vertical plane in a constant gravitational field. Let the origin of a coor- dinate system be located at some point in this plane. A particle of mass m moves in the vertical plane under the influence of gravity and under the influence of an ad- ditional force f= -Arª-¹ directed toward the origin (r is the distance from the origin; A and a [ 0 or 1] are constants). Choose appropriate generalized coordi- nates, and find the Lagrangian equations of motion. Is the angular momentum about the origin conserved? Explain.
7-5. Consider a vertical plane in a constant gravitational field. Let the origin of a coor- dinate system be located at some point in this plane. A particle of mass m moves in the vertical plane under the influence of gravity and under the influence of an ad- ditional force f= -Arª-¹ directed toward the origin (r is the distance from the origin; A and a [ 0 or 1] are constants). Choose appropriate generalized coordi- nates, and find the Lagrangian equations of motion. Is the angular momentum about the origin conserved? Explain.
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Theoretical Mechanics
Topic: Lagrangian and Hamiltonian Dynamics
>Generate the necessary equations to this system.
> Use the equations of motion
>Generate equations for (x,y), (Vx,Vy), V², T
> L = T-U
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For study purposes. Thank you!
![7-5. Consider a vertical plane in a constant gravitational field. Let the origin of a coor-
dinate system be located at some point in this plane. A particle of mass m moves in
the vertical plane under the influence of gravity and under the influence of an ad-
ditional force f= -Ara-1 directed toward the origin (r is the distance from the
origin; A and a [ 0 or 1] are constants). Choose appropriate generalized coordi-
nates, and find the Lagrangian equations of motion. Is the angular momentum
about the origin conserved? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e037703-16f1-40aa-84c7-090a0ffa9ec0%2F8f73f83c-11f9-4095-b7d1-46bc7aaf91bf%2Ff0um5769.jpeg&w=3840&q=75)
Transcribed Image Text:7-5. Consider a vertical plane in a constant gravitational field. Let the origin of a coor-
dinate system be located at some point in this plane. A particle of mass m moves in
the vertical plane under the influence of gravity and under the influence of an ad-
ditional force f= -Ara-1 directed toward the origin (r is the distance from the
origin; A and a [ 0 or 1] are constants). Choose appropriate generalized coordi-
nates, and find the Lagrangian equations of motion. Is the angular momentum
about the origin conserved? Explain.
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