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Consider in three-dimensional space a particle that moves at a central potential . Then the equation of motion of the particle is F=m((d^2)r/dt^2)=-∇U(|r|) Consider the transformation of the right-hand side of the equation, ∇U (r), in the Galileo transformation r ′ = r - vt and state that the equation of motion is a Galileo invariant.

Consider in three-dimensional space a particle that moves at a central potential . Then the equation of motion of the particle is F=m((d^2)r/dt^2)=-∇U(|r|) Consider the transformation of the right-hand side of the equation, ∇U (r), in the Galileo transformation r ′ = r - vt and state that the equation of motion is a Galileo invariant.

Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter14: Special Theory Of Relativity
Section: Chapter Questions
Problem 14.6P
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Consider in three-dimensional space a particle that moves at a central potential . Then the equation of motion of the particle is

F=m((d^2)r/dt^2)=-∇U(|r|)

Consider the transformation of the right-hand side of the equation, ∇U (r), in the Galileo transformation r ′ = r - vt and state that the equation of motion is a Galileo invariant.

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