Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

DOI

10.2991/jnmp.2007.14.4.3How to use a DOI?

Abstract

In this work we investigate a formal mapping between the dynamical properties of the unidimensional relativistic oscillator and the asymmetrical rigid top at a clas- sical level. We study the relativistic oscillator within Yamaleev’s interpretation of Nambu mechanics. Such interpretation is based on the factorisation of the momenta, and as a consequence of this factorisation we are led to a three dimensional phase space. Solutions of the relativistic oscillator are given in terms of the Jacobian elliptic functions and hence we establish a correspondence of these solutions in terms of well known quantities from the rigid body theory. We also study some mechanical restric- tions that appear in the mathematical development of the mapping. In particular, we find a lower bound for the relativistic frequency in order to make the mapping self-consistent and physically legitimate.

Copyright

© 2007, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - JOUR
AU  - Alberto Molgado
AU  - Adan Rodríguez
PY  - 2007
DA  - 2007/12/01
TI  - Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body
JO  - Journal of Nonlinear Mathematical Physics
SP  - 534
EP  - 547
VL  - 14
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2007.14.4.3
DO  - 10.2991/jnmp.2007.14.4.3
ID  - Molgado2007
ER  -