322Chapter 8 Two-Body Central-Force Problemspositive constants. (a) Find the Lagrangian in terms of the CM position R and the relative positionr₂. (b) Write down and solve the Lagrange equations for the CM and relative coordinatesX, Y and x, y. Describe the motion.r=r₁8.10 Two particles of equal masses mi = m₂ move on a frictionless horizontal surface in the vicinityof a fixed force center, with potential energies U₁ = kr? and U₂ = kr2. In addition, they interact witheach other via a potential energy U₁2 = akr², where r is the distance between them and a and k are-

The Lagrangian of the given system is,For m1=m2=m, the above equation can be written as follows:The…

Answered: 8.10** Two particles of equal masses m₁…

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