Abstract
Abstract In this paper, we have studied the equations of motion for the problem, which are regularised in the neighbourhood of one of the finite masses and the existence of periodic orbits in a three-dimensional coordinate system when μ = 0. Finally, it establishes the canonical set (l, L, g, G, h, H) and forms the basic general perturbation theory for the problem.
Highlights
In this paper, we wish to study the three-dimensional generalisation of the problem studied by Bhatnagar [12,13,14] for the circular case
We have presented an analytical study of the existence of periodic orbits for μ = 0 in the restricted problem of three
−1 > 0 and for the problem generated by this Hamiltonian, we have dL dτ
Summary
We wish to study the three-dimensional generalisation of the problem studied by Bhatnagar [12,13,14] for the circular case. Since the Hamilton-Jacobi equation for generating a solution takes an unmanageable form for any solution, we have assumed that the third coordinate (3 of the infinitesimal mass is of the 0(μ). It will be interesting to observe that various equations and results worked out by Bhatnagar can be deduced from our results. During the last few years, many mathematician and astronomers have studied different types of periodic orbits in the restricted problem. We have presented an analytical study of the existence of periodic orbits for μ = 0 in the restricted problem of three. Poddar and Sharma Applied Mathematics and Nonlinear Sciences 6(2021) 429–438 bodies in a three-dimensional coordinate system when the smaller primary is a triaxial rigid body
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