Infinitesimal Orbits Around the Libration Points in the Elliptic Restricted Three Body Problem |
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Authors: | Ashraf Hamdy Mostafa K Ahmed Mohamad Radwan Fawzy Ahmed Abd El-Salam |
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Institution: | (1) Faculty of Science, Department of Astronomy, Cairo University, Cairo, Egypt |
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Abstract: | The objective of the present work is to develope explicit analytical expressions for the small amplitude orbits of the infinitesimal
mass about the equilibrium points in the elliptic restricted three body problem. To handle this dynamical problem, the Hamiltonian
for the elliptic problem is formed with the true anomaly and then with the eccentric anomaly as independent variables. The
origin is then transformed to a fixed point and the Hamiltonian is developed up to O(4) in the eccentricity, e, (which plays the role of the small parameter of the problem) of the primaries. The integration of the model problem under
consideration is undertaken by means of a perturbation technique based on Lie series developments, which leads to the solution
of the canonical equations of motion. |
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Keywords: | |
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