Time-independent Hamiltonians describing systems with friction: the "cyclotron with friction". Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Calogero, Francesco; Leyvraz, François
• Is Part Of: Journal of nonlinear mathematical physics. Volume 26:Issue 1(2019)
• Page Start: 147
• Page End: 154
• Publication Date: 2019-01-02
• Subjects: Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2019.1544795
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : As is well-known, any ordinary differential equation in one dimension can be cast as the Euler–Lagrange equation of an appropriate Lagrangian. Additionally, if the initial equation is autonomous, the Lagrangian can always be chosen to be time-independent. In two dimensions, however, the situation is more complex, and there exist systems of ODEs which cannot be described by any Lagrangian. In this paper we display Hamiltonians which describe the behaviour of a charged particle moving in a plane under the combined influence of a constant electric field (in the plane) and a constant magnetic field (orthogonal to the plane) as well as a friction force proportional to the velocity ("cyclotron with friction").