Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body
- 10.2991/jnmp.2007.14.4.3How to use a DOI?
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 Yamaleevâ€™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.
- © 2007, the Authors. Published by Atlantis Press.
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- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
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 -