8.10** Two particles of equal masses m₁ = m₂ move on a frictionless horizontal surface in the vicinity of a fixed force center, with potential energies U₁=kr and U₂ = kr2. In addition, they interact with each other via a potential energy U₁2 = akr², where r is the distance between them and a and k are 322 Chapter 8 Two-Body Central-Force Problems positive constants. (a) Find the Lagrangian in terms of the CM position R and the relative position r=r₁ r₂. (b) Write down and solve the Lagrange equations for the CM and relative coordinates X, Y and x, y. Describe the motion.
8.10** Two particles of equal masses m₁ = m₂ move on a frictionless horizontal surface in the vicinity of a fixed force center, with potential energies U₁=kr and U₂ = kr2. In addition, they interact with each other via a potential energy U₁2 = akr², where r is the distance between them and a and k are 322 Chapter 8 Two-Body Central-Force Problems positive constants. (a) Find the Lagrangian in terms of the CM position R and the relative position r=r₁ r₂. (b) Write down and solve the Lagrange equations for the CM and relative coordinates X, Y and x, y. Describe the motion.
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Chapter 8 Two-Body Central-Force Problems
positive constants. (a) Find the Lagrangian in terms of the CM position R and the relative position
r₂. (b) Write down and solve the Lagrange equations for the CM and relative coordinates
X, Y and x, y. Describe the motion.
r=r₁
8.10 Two particles of equal masses mi = m₂ move on a frictionless horizontal surface in the vicinity
of a fixed force center, with potential energies U₁ = kr? and U₂ = kr2. In addition, they interact with
each other via a potential energy U₁2 = akr², where r is the distance between them and a and k are
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