Authors: Adrian Sfarti
Addresses: CS Department, UC Berkeley, 387 Soda Hall Berkeley, CA 94720-1776, USA
Abstract: A Lagrangian L of a dynamical system is a function that summarises the dynamics of the system (Goldstein et al., 2002). If the Lagrangian of a system is known, then the equations of motion of the system may be obtained by its direct substitution into the Euler-Lagrange equation. One important advantage of the Lagrange formulation of dynamical systems is that the formulation is not tied to any particular coordinate system – rather, any convenient set of variables may be used to describe the system. Finding the Lagrangian for a system is a mix of science and art. In the following paper we will demonstrate how to find it for the case of relativistic electrodynamics as a direct application for particle accelerators. We will show how we can start from the expression of the Lagrangian in classical electrodynamics in finding its expression for relativistic cases.
Keywords: Lagrangian; Hamiltonian; relativistic electrodynamics; particle accelerators.
International Journal of Nuclear Energy Science and Technology, 2010 Vol.5 No.3, pp.189 - 194
Available online: 02 Jun 2010 *Full-text access for editors Access for subscribers Purchase this article Comment on this article