m, m . Two particles of equal masses move on a frictionless harizontal surface. Their center of krị - mass is fixed and their potential energies are krž Also, they interact with each and akr other with potential R is the distance between the masses, and k and a are positive constants. a. Find the Lagrangian in terms of the center of mass position CM, R and the relative position r. b. Solve the Lagrange equations for the relative coordinates X,Y and x,y. C. Explain the physical outcome of the results obtained in b.

m, m . Two particles of equal masses move on a frictionless harizontal surface. Their center of krị - mass is fixed and their potential energies are krž Also, they interact with each and akr other with potential R is the distance between the masses, and k and a are positive constants. a. Find the Lagrangian in terms of the center of mass position CM, R and the relative position r. b. Solve the Lagrange equations for the relative coordinates X,Y and x,y. C. Explain the physical outcome of the results obtained in b.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

m, zm
2. Two particles of equal masses move on a frictionless harizontal surface. Their center of
kr?
mass is fixed and their potential energies are
krž
and
Also, they interact with each
other with potential
2
akr2
Ris the distance between the masses, and k and a are positive
constants.
a. Find the Lagrangian in terms of the center of mass position CM, R and the relative
position r.
b. Solve the Lagrange equations for the relative coordinates X,Y and x,y.
c. Explain the physical outcome of the results obtained in b.

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