Solution of the Hamilton – Jacobi Equations in an Electromagnetic Field Using Separation of Variables Method – Staeckel Boundary Conditions

Abstract

This manuscript aims to resolve the Hamilton-Jacobi equations in an electromagnetic field by two methods. The first uses the separation of variables technique with Staeckel boundary conditions, whereas the second uses the Newtonian formalism to solve the same example. Our results demonstrate that the Hamilton-Jacobi variables can be completely detached by using separation of variables technique with Staeckel boundary conditions that correspond to other results using Newtonian formalism.

Keywords: Lagrangian mechanics, Electromagnetic field, Hamilton-Jacobi, Staeckel boundary conditions, Newtonian mechanics.