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On the symmetry of Hamiltonian systems
(Maltepe Üniversitesi, 2009) Gupta, V. G.; Sharma, P.
In this paper, we use the formalism of Hamiltonian system on symplectic manifold due to Reeb[2] given in Abraham and Marsden[6] and Arnold[7] to derive the equation of motion for (1) A particle on a line in a plane with a spring force and (2) 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.
Solving singular initial value problems of emden-fowler and lane-emden type
(Maltepe Üniversitesi, 2009) Gupta, V. G.; Sharma, P.
In this paper, Singular initial value problems are investigated by using Taylor series method. The solutions are constructed in the form of a convergent series. The method is applied to Emden-Fowler and Lane-Emden equations.