Classical Mechanics Problem-1: Consider three particles of the ... | Filo (2024)

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Question Text

Classical MechanicsProblem-1: Consider three particles of the same mass m moving in one dimension (let's say along the r-axis) and interacting with each other via the potential U = U(-a), where a labels the coordinate of the ith particle. Show by explicit computation that in addition to the conserved total momentum of all particles P = m(1+2+3), and total energy E = (1/2)m(1^2+2^2+3^2) + U12 + U23 + U31, there exists an additional integral of motion:A = m(1^2+2^2+3^2) - U23 - 2U31 - 3U21(1)for the special case of interaction potential Uik = g/(ri - rj)^2, where g is some constant. [2 points]

TopicAll topics
SubjectPhysics
ClassClass 11
Classical Mechanics
Problem-1: Consider three particles of the ... | Filo (2024)
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