Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T04:18:05.169Z Has data issue: false hasContentIssue false
  • English
  • Français

On relative equilibria of mutually gravitating massive point and triangular rigid body

Published online by Cambridge University Press:  05 January 2015

Vasily I. Nikonov
Vasily I. Nikonov*
Affiliation:
Lomonosov Moscow State University, Department of Mechanics and Mathematics email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Planar motions of a triangular body and a massive point under the action of mutual Newtonian attraction are studied. For the first formulation the triangle is assumed to be composed of three massive points. For the second formulation it is constructed with three homogeneous rods. Some partial solutions are observed within the analysis of the geometry of mass distribution.

The investigation is motivated by the problem of motion of spacecrafts near asteroid-like celestial objects possessing irregular mass distribution. Comparison of dynamical effects for two types of mass distribution is another goal of the research.

Problems appearing because of irregularities in mass distributions have been known for a long time. Certain approaches to the description of motions under attraction as well as qualitative particulars of dynamics are discussed by Demin (1963), Burov & Karapetyan (1995), Buchin & Burov & Troger (2008), Burov & Guerman & Sulikashvili (2010), Kholshevnikov & Kuznetsov (2011), Beletsky & Rodnikov (2011) and Scheeres (2012).

Keywords

celestial mechanicsgeneralized two-body problemrelative equilibriastabilityPoincaré bifurcation diagrambarycentric coordinates
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 9 , Issue S310: Complex Planetary Systems , July 2014 , pp. 170 - 171
Copyright
Copyright © International Astronomical Union 2014 

References

Aksenov, E. P., Grebenikov, E. A., & Demin, V. G. 1963, Soviet Astron., 7, 276Google Scholar
Burov, A. A. & Karapetyan, A. V. 1995, Mechanics of solids, 30, 14Google Scholar
Burov, A. A., Guerman, A. D., & Sulikashvili, R. S. 2010, Dynamics of a Tetrahedral Satellite-Gyrostat, AIP Conference Proceedings, ICNAAM 2010, 1281, 465Google Scholar
Kholshevnikov, K. V. & Kuznetsov, E. D. 2011, Celest. Mech. Dyn. Astr., 109, 201Google Scholar
Scheeres, D. J. 2012, Orbital Motion in Strongly Perturbed Environmentss Berlin: Springer. 390 p.Google Scholar
Beletsky, V. & Rodnikov, A. 2011, Proc. of 5th PhysCon Leon Spain.Google Scholar
Buchin, V., Burov, A., & Troger, H. 2008, 6th EUROMECH Nonlinear Dynamics Conference. ENDC 2008, IPME RAS.Google Scholar
Routh, E. J. 1877, Treatise on the Stability of a Given State of Motion. L: MacMillan.Google Scholar
Nikonov, V. 2014, Moscow University Mechanics Bulletin, 69, 44Google Scholar