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Dynamics of a point in the axisymmetric gravitational potential of a massive fixed ring and center
A. V. Sakharov Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Oblast, Russia
Abstract:
We consider the problem of three-dimensional motion of a passively gravitating point in the potential created by a homogeneous thin fixed ring and a massive point located in the center of the ring. The motion of a passively gravitating point admits two first integrals. We first consider the integrable case of an invariant motion in the equatorial plane and then consider the general case of three-dimensional motion, where we classify the possible trajectories of a point depending on the values of the first integrals. Finally, some previous results for similar problems are compared.
Keywords:
celestial mechanics, axisymmetric potential, gravitational potential, ring, phase portrait, first integral, bifurcation.
Received: 04.12.2020 Revised: 31.12.2020
Citation:
A. V. Sakharov, “Dynamics of a point in the axisymmetric gravitational potential of a massive fixed ring and center”, TMF, 207:2 (2021), 319–330; Theoret. and Math. Phys., 207:2 (2021), 678–688
Linking options:
https://www.mathnet.ru/eng/tmf10020https://doi.org/10.4213/tmf10020 https://www.mathnet.ru/eng/tmf/v207/i2/p319
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Abstract page: | 288 | Full-text PDF : | 36 | References: | 44 | First page: | 10 |
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