Journal of Nonlinear Mathematical Physics

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Volume 26, Issue 1, December 2018, Pages 147 - 154

Time-independent Hamiltonians describing systems with friction: the “cyclotron with friction”

Authors
Francesco Calogero*
Dipartimento di Fisica, Università di Roma “La Sapienza” Rome, 00185, Italy,francesco.calogero@roma1.infn.it;francesco.calogero@uniroma1.it
François Leyvraz†
Instituto de Ciencias Físicas, University of Mexico, Av. Universidad s/n, colonia Chamilpa Cuernavaca, 62210, Mexico,leyvraz@fis.unam.mx;f_leyvraz2001@hotmail.com
*also at Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy
†also at Centro Internacional de Ciencias, Cuernavaca, México
Corresponding Authors
Francesco Calogero, François Leyvraz
Received 27 July 2018, Accepted 15 September 2018, Available Online 6 January 2021.
DOI
10.1080/14029251.2019.1544795How to use a DOI?
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”).

Copyright
© 2019 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
26 - 1
Pages
147 - 154
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2019.1544795How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Francesco Calogero
AU  - François Leyvraz
PY  - 2021
DA  - 2021/01/06
TI  - Time-independent Hamiltonians describing systems with friction: the “cyclotron with friction”
JO  - Journal of Nonlinear Mathematical Physics
SP  - 147
EP  - 154
VL  - 26
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1544795
DO  - 10.1080/14029251.2019.1544795
ID  - Calogero2021
ER  -