Abstract

In this paper we research the orbital motion described by equations in hamiltonian form. The shift mapping along a trajectory of motion is canonical one and it makes possible to apply conservative methods. The examples of application of such methods in problems of celestial mechanics are given. The first order approximation of generating function of shift mapping along the trajectory is constructed for uncontrolled motion in a neighborhood of collinear libration point of Sun-Earth system. Also this approach is applied to controllable motion with special kind of control, which ensuring the preservation of hamiltonian form of the equations of motion. The form of iterative schemes for numerical modeling of motion is given. For fixed number of iterations the accuracy of presented numerical method is estimated in comparison with Runge-Kutta method of the fourth order. The analytical representation of the generating function up to second-order terms with respect to time increment is given.

Original languageEnglish
Title of host publicationApplication of Mathematics in Technical and Natural Sciences
Subtitle of host publication9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017
EditorsMD Todorov
PublisherAmerican Institute of Physics
Number of pages6
Volume1895
ISBN (Electronic)9780735415799
DOIs
Publication statusPublished - 2017
Event9th International Conference on Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS) - Albena
Duration: 21 Jun 201726 Jun 2017

Publication series

NameAIP Conference Proceedings
PublisherAMER INST PHYSICS
Volume1895
ISSN (Print)0094-243X

Conference

Conference9th International Conference on Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS)
CountryBulgaria
CityAlbena
Period21/06/1726/06/17

Scopus subject areas

  • Physics and Astronomy(all)

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    Shmyrov, A., Shmyrov, V., & Shymanchuk, D. (2017). The Research of Motion in a Neighborhood of Collinear Libration Point by Conservative Methods. In MD. Todorov (Ed.), Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017 (Vol. 1895). [060003] (AIP Conference Proceedings; Vol. 1895). American Institute of Physics. https://doi.org/10.1063/1.5007388