Using Hamiltonian mechanics, find the Lagrangian and the equations of motion for a particle of mass m moving in a central force field with potential energy given by V(r) = -k/r^n, where r is the radial distance from the center of the force, k is a positive constant, and n is a positive integer. Assume that the particle is moving in a two-dimensional plane. Show that the equations of motion are separable and solve for the general solution for the radial and angular coordinates of the particle in terms of its conserved energy and angular momentum.

Answer rating: 100% (QA)

The detailed answer for the above question is provided below Consider a particle of mass m moving in ... View the full answer