Open AccessDiagonalization of Hamiltonian in the photogravitation-al restricted three body problem with P-R drag
Author(s) -
Xavier James Raj,
B. Ishwar
Publication year - 2017
Publication title -
international journal of advanced astronomy
Language(s) - English
Resource type - Journals
ISSN - 2312-7414
DOI - 10.14419/ijaa.v5i2.7931
Subject(s) - hamiltonian (control theory) , hamiltonian system , mathematics , drag , lagrangian , taylor series , lagrangian point , three body problem , mathematical physics , power series , equilibrium point , quadratic equation , mathematical analysis , physics , classical mechanics , geometry , mathematical optimization , mechanics , differential equation
In this paper, restricted, three-body problem (RTBP) is generalised to study the non-linear stability of equilibrium points in the photogravitational RTBP with P-R drag. In the present study, both primaries are considered as a source of radiation and effect of P-R drag. Hence the problem will contain four parameters q1, q2, W1 and W2. At first, the Lagrangian and the Hamiltonian of the problem were computed, then the Lagrangian function is expanded in power series of the coordinates of the triangular equilibrium points x and y. Lastly, diagonalized the quadratic term of the Hamiltonian of the problem, which is obtained by expanding original Lagrangian or Hamiltonian by Taylor's series about triangular equilibrium point. Finally, the study concluded that the diagonalizable Hamiltonian is H2=ω1I1-ω2I2.