The two fixed centers problem: an integrable Hamiltonian system

Manem, Venkata Satya Kumar (2009) The two fixed centers problem: an integrable Hamiltonian system. Masters thesis, Memorial University of Newfoundland.

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Abstract

This thesis concerns the dynamical system of the two fixed centers problem restricted to a 2-D case. We use the Hamiltonian approach to find an analytical solution in terms of elliptical coordinates. A detailed analysis of quadratic polynomials whose roots control elliptic integrals involved is discussed. The theory is applied to the analysis of concrete orbits and the predictions of the theory are compared with results of direct numerical integration. We present two applications of the theory. One application is to find the escape velocities of the particle. The second application is to investigate the initial data for the particle to hit one of the fixed masses. The difference between the integrable system with Newtonian potential and a non-integrable system corresponding to the logarithmic potential is presented using the Poincare section technique.

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