In Exercise 1, there is given the velocity-dependent potential assumed in Weber’s electrod...

In Exercise 1, there is given the velocity-dependent potential assumed in Weber’s electrodynamics. What is the Hamiltonian for a single particle moving under the influence of such a potential?

Exercise 1

A particle moves in a plane under the influence of a force, acting toward a center of force, whose magnitude is

where r is the distance of the particle to the center of force. Find the generalized potential that will result in such a force, and from that the Lagrangian for the motion in a plane. (The expression for F represents the force between two charges in Weber’s electrodynamics.)