Lagrangian relative equilibria for a gyrostat in the three-body problem

• Authors: Juan López
• Languages of publication: EN

Abstracts

EN

In this paper we consider the noncanonical Hamiltonian dynamics of a gyrostat in the three-body problem. By means of geometric mechanics methods, we study the approximate Poisson dynamics that arise when we develop the potential of the system in Legendre series and truncate this to an arbitrary order k. After reduction of the dynamics by means of the two symmetries of the system, we consider the existence and number of equilibria which we denominate of Lagrangian type, in analogy with classic results on the topic. Necessary and sufficient conditions are established for their existence in an approximate dynamics of order k, and explicit expressions for these equilibria are given, this being useful for the subsequent study of their stability. The number of Lagrangian equilibria is thoroughly studied in approximate dynamics of orders zero and one. The main result of this work indicates that the number of Lagrangian equilibria in an approximate dynamics of order k for k ≥1 is independent of the order of truncation of the potential, if the gyrostat S
0 is almost spherical. In relation to the stability of these equilibria, necessary and sufficient conditions are given for linear stability of Lagrangian equilibria when the gyrostat is almost spherical. In this way, we generalize the classical results on equilibria of the three-body problem and many results provided by other authors using more classical techniques for the case of rigid bodies.

Keywords

EN

hamiltonian system; three-body problem; gyrostat; lagrangian equilibria; stability

Discipline

• 45.20.dc: Rotational dynamics
• 45.20.Jj: Lagrangian and Hamiltonian mechanics
• 45.40.-f: Dynamics and kinematics of rigid bodies
• 45.50.Pk: Celestial mechanics(see also 95.10.Ce in fundamental astronomy)
• 47.10.Df: Hamiltonian formulations

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2009
• Volume: 7
• Issue: 4
• Pages: 677-689

Dates

published

1 - 12 - 2009

online

21 - 7 - 2009

Contributors

author

Juan López

• I. E. S. O No. 2 de Fuente Álamo, Consejería de Educación y Cultura, Murcia, Spain

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Identifiers

DOI

10.2478/s11534-009-0040-x