Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 25 No. 1 (2007): Revista Integración, temas de matemáticas
Research and Innovation Articles

The Classical Isotropic bi-Dimensional Oscilator in the Eisenhart Formulation of Classical Mechanics

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  • U. Percoco,
  • L. A. Nuñez,
  • M. Zambrano
U. Percoco
Grupo de Física Teórica, Departamento de Física, Fac. de Ciencias Universidad de los Andes
L. A. Nuñez
Centro de Física Fundamental, Departamento de Física, Facultad de Ciencias, Universidad de Los
M. Zambrano
Grupo de Física Teórica, Departamento de Física, Fac. de Ciencias Universidad de los Andes

Published 2007-04-30

Keywords

  • Geometric Mechanics,
  • Geometrical and tensorial methods,
  • Formalisms in classical mechanics

How to Cite

Percoco, U., Nuñez, L. A., & Zambrano, M. (2007). The Classical Isotropic bi-Dimensional Oscilator in the Eisenhart Formulation of Classical Mechanics. Revista Integración, Temas De matemáticas, 25(1), 39–44. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/261

Abstract

Accordingly with the general theory of relativity, the motion of a particle by the only action of inertia and gravity is described by a space-time geodesic. We use the Eisenhart geometric formulation of classical mechanics to establish a correspondence between geodesics and paths in phase space of the classical bi-dimensional isotropic oscillator. The Killing vectors and its associated constants of motion are presented and compared with nonNoetherian motion constant calculated by S. Hojman and collaborators.

 

Keywords: Geometric Mechanics, Geometrical and tensorial methods, Formalisms in classical mechanics.

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References

[1] S. Hojman, J. Phys. A: Math. Gen. 17, 2399 (1984).

[2] S. Hojman, F. Zertuche, Novo Cimento Soc. Ital. Fis. B, 88, 1 (1985).