Consider a vertical plane in a constant gravitational field. Let the origin of a coordinate 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 addition force f =-Ar"- directed toward the origin (r is the distance from the origin; A and a [#0 or 1] are constants). Choose appropriate generalized coordinates, and find the Lagrangian equations of motion (don't solve it). Is the angular momentum about the origin conserved? Explain.
Consider a vertical plane in a constant gravitational field. Let the origin of a coordinate 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 addition force f =-Ar"- directed toward the origin (r is the distance from the origin; A and a [#0 or 1] are constants). Choose appropriate generalized coordinates, and find the Lagrangian equations of motion (don't solve it). Is the angular momentum about the origin conserved? Explain.
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![1. Consider a vertical plane in a constant gravitational field. Let the origin of a
coordinate 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
addition force f = -Ar"- directed toward the origin (r is the distance from the
origin; A and a [#0 or 1] are constants). Choose appropriate generalized coordinates,
and find the Lagrangian equations of motion (don't solve it). Is the angular
momentum about the origin conserved? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2Fccc32979-fc3a-450d-a314-3e23b7d669f3%2Fv0n43f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider a vertical plane in a constant gravitational field. Let the origin of a
coordinate 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
addition force f = -Ar"- directed toward the origin (r is the distance from the
origin; A and a [#0 or 1] are constants). Choose appropriate generalized coordinates,
and find the Lagrangian equations of motion (don't solve it). Is the angular
momentum about the origin conserved? Explain.
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