Some solutions of the general three body problem in form space

Research outputpeer-review

Abstract

Some solutions of three body problem with equal masses are first considered in form space. The solutions in usual euclidean space may be restored from these form space solutions. If constant energy h < 0, the trajectories are located inside of Hill's surface. Without loss of generality due to scale symmetry we can set h = -1. Such surface has a simple form in form space. Solutions of isosceles and rectilinear three body problems lie within Hill's curve; periodic solutions of free fall three body problem start in one point of this curve, and finish in another. The solutions are illustrated by number of figures.

Original languageEnglish
Title of host publication8th Polyakhov's Reading
Subtitle of host publicationProceedings of the International Scientific Conference on Mechanics
EditorsElena V. Kustova, Gennady A. Leonov, Mikhail P. Yushkov, Nikita F. Morosov, Mariia A. Mekhonoshina
PublisherAmerican Institute of Physics
Volume1959
ISBN (Electronic)9780735416604
DOIs
Publication statusPublished - 2 May 2018
EventInternational Scientific Conference on Mechanics: 8th Polyakhov's Reading - Saint Petersburg
Duration: 29 Jan 20182 Feb 2018

Conference

ConferenceInternational Scientific Conference on Mechanics: 8th Polyakhov's Reading
CountryRussian Federation
CitySaint Petersburg
Period29/01/182/02/18

Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Titov, V. (2018). Some solutions of the general three body problem in form space. In E. V. Kustova, G. A. Leonov, M. P. Yushkov, N. F. Morosov, & M. A. Mekhonoshina (Eds.), 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics (Vol. 1959). [040024] American Institute of Physics. https://doi.org/10.1063/1.5034627
Titov, Vladimir. / Some solutions of the general three body problem in form space. 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. editor / Elena V. Kustova ; Gennady A. Leonov ; Mikhail P. Yushkov ; Nikita F. Morosov ; Mariia A. Mekhonoshina. Vol. 1959 American Institute of Physics, 2018.
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Titov, V 2018, Some solutions of the general three body problem in form space. in EV Kustova, GA Leonov, MP Yushkov, NF Morosov & MA Mekhonoshina (eds), 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. vol. 1959, 040024, American Institute of Physics, Saint Petersburg, 29/01/18. https://doi.org/10.1063/1.5034627

Some solutions of the general three body problem in form space. / Titov, Vladimir.

8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. ed. / Elena V. Kustova; Gennady A. Leonov; Mikhail P. Yushkov; Nikita F. Morosov; Mariia A. Mekhonoshina. Vol. 1959 American Institute of Physics, 2018. 040024.

Research outputpeer-review

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Titov V. Some solutions of the general three body problem in form space. In Kustova EV, Leonov GA, Yushkov MP, Morosov NF, Mekhonoshina MA, editors, 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. Vol. 1959. American Institute of Physics. 2018. 040024 https://doi.org/10.1063/1.5034627