A. V. Borisov, I. S. Mamaev, A. A. Kilin, “Two-body problem on a sphere. Reduction, stochasticity, periodic orbits”, Regul. Chaotic Dyn., 9:3 (2004), 265

Regular and Chaotic Dynamics

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ЖУРНАЛЫ ПЕРСОНАЛИИ ОРГАНИЗАЦИИ КОНФЕРЕНЦИИ СЕМИНАРЫ ВИДЕОТЕКА ПАКЕТ AMSBIB

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Regular and Chaotic Dynamics, 2004, том 9, выпуск 3, страницы 265–279
DOI: https://doi.org/10.1070/RD2004v009n03ABEH000280 (Mi rcd746)

Эта публикация цитируется в 42 научных статьях (всего в 42 статьях)

Effective computations in modern dynamics

Two-body problem on a sphere. Reduction, stochasticity, periodic orbits

A. V. Borisov, I. S. Mamaev, A. A. Kilin

Institute of Computer Science, Udmurt State University, Universitetskaya, 1, 426034, Izhevsk, Russia

Список цитирования (42)

DOI: https://doi.org/10.1070/RD2004v009n03ABEH000280

Аннотация: We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a system with two degrees of freedom and give a number of remarkable periodic orbits. We also discuss integrability and stochastization of the motion.

Поступила в редакцию: 25.06.2004

Реферативные базы данных:

Тип публикации: Статья

MSC: 37N05, 70F10

Язык публикации: английский

Образец цитирования: A. V. Borisov, I. S. Mamaev, A. A. Kilin, “Two-body problem on a sphere. Reduction, stochasticity, periodic orbits”, Regul. Chaotic Dyn., 9:3 (2004), 265–279

Цитирование в формате AMSBIB

\RBibitem{BorMamKil04}

\by A. V. Borisov, I. S. Mamaev, A. A. Kilin

\paper Two-body problem on a sphere. Reduction, stochasticity, periodic orbits

\jour Regul. Chaotic Dyn.

\yr 2004

\vol 9

\issue 3

\pages 265--279

\mathnet{http://mi.mathnet.ru/rcd746}

\crossref{https://doi.org/10.1070/RD2004v009n03ABEH000280}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2104172}

\zmath{https://zbmath.org/?q=an:1065.37058}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004RCD.....9..265B}

Образцы ссылок на эту страницу:

https://www.mathnet.ru/rus/rcd746

https://www.mathnet.ru/rus/rcd/v9/i3/p265

Эта публикация цитируется в следующих 42 статьяx:

Rubén Darío Ortiz Ortiz, Ana Magnolia Marín Ramírez, Ismael Oviedo de Julián, “Asymptotic Antipodal Solutions as the Limit of Elliptic Relative Equilibria for the Two- and n-Body Problems in the Two-Dimensional Conformal Sphere”, Mathematics, 12:7 (2024), 1025
Toshiaki Fujiwara, Ernesto Pérez-Chavela, “Mass-Independent Shapes for Relative Equilibria in the Two-Dimensional Positively Curved Three-Body Problem”, J Nonlinear Sci, 34:5 (2024)
Toshiaki Fujiwara, Ernesto Pérez-Chavela, “Continuations and Bifurcations of Relative Equilibria for the Positively Curved Three-Body Problem”, Regul. Chaotic Dyn., 29:6 (2024), 803–824
Shuqiang Zhu, “The Schubart Orbits in the Curved Three-Body Problem with Two Equal Masses”, J Nonlinear Sci, 34:6 (2024)
Toshiaki Fujiwara, Ernesto Pérez-Chavela, “Three-Body Relative Equilibria on $\mathbb{S}^2$ ”, Regul. Chaotic Dyn., 28:4-5 (2023), 690–706
Pieter Tibboel, “Classification of positive elliptic-elliptic rotopulsators on Clifford tori”, Journal of Mathematical Analysis and Applications, 526:1 (2023), 127154
Zhu Sh., “Dziobek Equilibrium Configurations on a Sphere”, J. Dyn. Differ. Equ., 34:2 (2022), 1269–1283
Carlos García-Azpeitia, Luis C. García-Naranjo, “Platonic Solids and Symmetric Solutions of the N-vortex Problem on the Sphere”, J Nonlinear Sci, 32:3 (2022)
Juan Manuel Sánchez-Cerritos, Liang Ding, Jinlong Wei, “Equilibrium points in restricted problems on S2 and H2”, Journal of Mathematical Physics, 63:6 (2022)
Antonio Hernández-Garduño, Ernesto Pérez-Chavela, Shuqiang Zhu, “Stability of Regular Polygonal Relative Equilibria on $\mathbf{}\mathbb S^2$ ”, J Nonlinear Sci, 32:5 (2022)
Juan Manuel Sánchez-Cerritos, Ernesto Pérez-Chavela, “Hyperbolic regularization of the restricted three–body problem on curved spaces”, Anal.Math.Phys., 12:1 (2022)
Garcia-Naranjo L.C. Montaldi J., “Attracting and Repelling 2-Body Problems on a Family of Surfaces of Constant Curvature”, J. Dyn. Differ. Equ., 33:4 (2021), 1579–1603
Yu X., Zhu Sh., “Regular Polygonal Equilibria on S-1 and Stability of the Associated Relative Equilibria”, J. Dyn. Differ. Equ., 33:2 (2021), 1071–1086
Shuqiang Zhu, “Compactness and Index of Ordinary Central Configurations for the Curved $N$ -Body Problem”, Regul. Chaotic Dyn., 26:3 (2021), 236–257
Nataliya A. Balabanova, James A. Montaldi, “Two-body Problem on a Sphere in the Presence of a Uniform Magnetic Field”, Regul. Chaotic Dyn., 26:4 (2021), 370–391
Jaime Andrade, Claudio Vidal, Claudio Sierpe, “Stability of the Relative Equilibria in the Two-body Problem on the Sphere”, Regul. Chaotic Dyn., 26:4 (2021), 402–438
Jackman C., “Secular Dynamics For Curved Two-Body Problems”, J. Dyn. Differ. Equ., 2021
Garcia-Naranjo L.C., “Some Remarks About the Centre of Mass of Two Particles in Spaces of Constant Curvature”, J. Geom. Mech., 12:3 (2020), 435–446
Tibboel P., “Results on Equality of Masses For Choreographic Solutions of N-Body Problems”, J. Math. Phys., 61:9 (2020), 092901
Sanchez-Cerritos J.M., “Local Regularization of a Restricted Problem on H-2 With Primaries on Hyperbolic Motion”, J. Geom. Phys., 157 (2020), 103806

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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