The Sitnikov problem for manev type potentials

dc.contributor.author	Verjinschi, Bogdan	en_US
dc.date.accessioned	2024-08-15T20:11:55Z
dc.date.available	2024-08-15T20:11:55Z
dc.date.copyright	2003	en_US
dc.date.issued	2003
dc.degree.department	Department of Mathematics and Statistics	en_US
dc.degree.level	Master of Science M.Sc.	en
dc.description.abstract	This thesis focuses on how the Sitnikov problem changes if the classical Newtonian potential is replaced by a relativist potential of the Manev type. Considering initially the movement of the two primaries only, we study how replacing the potential will affect their trajectories. We establish the condition for closed trajectories for the movement of the primaries. The Sitnikov problem for Manev-type potential is a relativistic perturbation of the classical Newtonian potential, a particular case of the Manev three-body problem with two primaries moving on precessional ellipses and a third negligible mass that oscillates on an axis passing through their centre of mass, perpendicularly to their plane of motion. We use Melnikov's theory to prove the existence of transverse homoclinic orbits for at least a discrete set of initial conditions, showing that in those cases the motion is very complicated, thus extending a result obtained by Dankowikz and Holmes in the classical Newtonian case.
dc.format.extent	59 pages
dc.identifier.uri	https://hdl.handle.net/1828/19991
dc.rights	Available to the World Wide Web	en_US
dc.title	The Sitnikov problem for manev type potentials	en_US
dc.type	Thesis	en_US

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