Subscribe Now Subscribe Today
Science Alert
 
Blue
   
Curve Top
Asian Journal of Earth Sciences
  Year: 2009 | Volume: 2 | Issue: 2 | Page No.: 39-48
DOI: 10.3923/ajes.2009.39.48
 
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail

Symmetry of Hamiltonian Systems

V.G. Gupta and P. Sharma

Abstract:
In the present study we use the formalism of Hamiltonian system on symplectic manifold due to Reeb, given in Abraham and Marsden and Arnold to derive the equation of motion for a particle on a line in a plane with a spring force and for a free particle in n-space. The time flows for both the problems mentioned above are also determined and proved that the determined flow is a Hamiltonian flow i.e., the symmetry of a Hamiltonian system. A non-Hamiltonian flow is also considered and it is shown that by changing the symplectic form and the phase space of the system we can convert it into a Hamiltonian flow. The translation and rotational symmetry related to linear and angular momentum respectively for the motion of a free particle in n-space is also considered, which is useful in reducing the phase space of a mechanical system.
PDF Fulltext XML References Citation Report Citation
How to cite this article:

V.G. Gupta and P. Sharma, 2009. Symmetry of Hamiltonian Systems. Asian Journal of Earth Sciences, 2: 39-48.

DOI: 10.3923/ajes.2009.39.48

URL: https://scialert.net/abstract/?doi=ajes.2009.39.48

COMMENT ON THIS PAPER
 
 
 

 

 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 

Curve Bottom