A particle moves in a plane under the influence of a force f= -Ara-1 directed to- ward the origin; A and a (> 0) are constants. Choose appropriate generalized co- ordinates, and let the potential energy be zero at the origin. Find the Lagrangian equations of motion. Is the angular momentum about the origin conserved? Is the total energy conserved?
A particle moves in a plane under the influence of a force f= -Ara-1 directed to- ward the origin; A and a (> 0) are constants. Choose appropriate generalized co- ordinates, and let the potential energy be zero at the origin. Find the Lagrangian equations of motion. Is the angular momentum about the origin conserved? Is the total energy conserved?
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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!
Transcribed Image Text:7-4.
A particle moves in a plane under the influence of a force f= -Ara-¹ directed to-
ward the origin; A and a (> 0) are constants. Choose appropriate generalized co-
ordinates, and let the potential energy be zero at the origin. Find the Lagrangian
equations of motion. Is the angular momentum about the origin conserved? Is the
total energy conserved?
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