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Astrodynamics 2017, 1(1): 41-55 https://doi.org/10.1007/s42064-017-0004-7
Research Article | Issue | Published: 08 September 2017

Periodic orbits in the Chermnykh problem

Show Author's Information Xiangyuan Zeng1( ),  Kyle T. Alfriend2
School of Automation, Beijing Institute of Technology, Beijing 100081, China
Department of Aerospace Engineering, Texas A&M University, College Station, Texas 77840, USA
Keywords:
periodic orbits, the Chermnykh problem, topological transition, iso-energetic continuation
Cite this article:
Zeng X, Alfriend KT. Periodic orbits in the Chermnykh problem. Astrodynamics, 2017, 1(1): 41-55. https://doi.org/10.1007/s42064-017-0004-7
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Abstract Full text About this article

Periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as the engineering aspect for deep space explorations. The rotating mass dipole, referred to as the Chermnykh problem, is a good alternative model to study qualitative dynamical environments near elongated asteroids, like the asteroid 1620 Geographos, 216 Kleopatra, or 25143 Itokawa. In this paper a global searching method is adopted to search for periodic orbits around the dipole model based on the concept of Poincaré section of surface. Representative families of periodic orbits are illustrated with respect to all three topological cases of the dipole model. Topological transitions of orbits during iso-energetic continuations are also presented as well as identification of new types of periodic orbits.


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About this article

Periodic orbits in the Chermnykh problem

Show Author's information Xiangyuan Zeng1( ), Kyle T. Alfriend2
School of Automation, Beijing Institute of Technology, Beijing 100081, China
Department of Aerospace Engineering, Texas A&M University, College Station, Texas 77840, USA

Abstract

Periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as the engineering aspect for deep space explorations. The rotating mass dipole, referred to as the Chermnykh problem, is a good alternative model to study qualitative dynamical environments near elongated asteroids, like the asteroid 1620 Geographos, 216 Kleopatra, or 25143 Itokawa. In this paper a global searching method is adopted to search for periodic orbits around the dipole model based on the concept of Poincaré section of surface. Representative families of periodic orbits are illustrated with respect to all three topological cases of the dipole model. Topological transitions of orbits during iso-energetic continuations are also presented as well as identification of new types of periodic orbits.

Keywords: periodic orbits, the Chermnykh problem, topological transition, iso-energetic continuation

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Publication history
Copyright
Acknowledgements

Publication history

Received: 21 November 2016
Accepted: 16 January 2017
Published: 08 September 2017
Issue date: March 2017

Copyright

© Tsinghua University Press 2017

Acknowledgements

Thanks for the thoughtful discussions and suggestions of Yanshuo Ni and Prof. Junfeng Li from Tsinghua University, Beijing, China. This work was supported by the National Natural Science Foundation of China (No. 11602019). The Excellent Young Teachers Program of Beijing Institute of Technology (No. 2015YG0605) and Beijing Institute of Technology Research Fund Program for Young Scholars were also acknowledged.

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