Asian Journal of Earth Sciences1819-18862152-3509Academic Journals Inc.10.3923/ajes.2009.39.48GuptaV.G.SharmaP.2200922In 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.]]>Abraham, R. and J. Marsden,1978Arnold, V.I.,1989Artin, M.,1991Cartan, E.,1922Marsden, J.E. and T.S. Ratiu,1999Reeb, G.,1952Simmons, G.F.,1991