Qualitative analysis of the phase flow of an integrable approximation of a generalized roto-translatory problem

• Authors: María Balsas , Elena Jiménez , Juan Vera , Antonio Vigueras
• Languages of publication: EN

Abstracts

EN

In this paper, we consider an integrable approximation of the planar motion of a gyrostat in Newtonian interaction with a spherical rigid body. We then describe the Hamiltonian dynamics, in the fibers of constant total angular momentum vector of an invariant manifold of motion. Finally, using the Liouville-Arnold theorem and a particular analysis of the momentum map in its critical points, we obtain a complete topological classification of the different invariant sets of the phase flow of this problem. The results can be applied to study two-body roto-translatory problems where the rotation of one of them has a strong influence on the orbital motion of the system.

Keywords

EN

Liouville-Arnold theorem; gyrostat; invariant manifolds; amended potential; Hill regions

Discipline

• 45.20.dc: Rotational dynamics
• 45.20.Jj: Lagrangian and Hamiltonian mechanics
• 45.40.Cc: Rigid body and gyroscope motion
• 45.50.Pk: Celestial mechanics(see also 95.10.Ce in fundamental astronomy)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2009
• Volume: 7
• Issue: 1
• Pages: 67-78

Dates

published

1 - 3 - 2009

online

8 - 1 - 2009

Contributors

author

María Balsas

• Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena (Murcia), Spain

author

Elena Jiménez

• Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena (Murcia), Spain

author

Juan Vera

• Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena (Murcia), Spain

author

Antonio Vigueras

• Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena (Murcia), Spain

References

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Identifiers

DOI

10.2478/s11534-008-0140-z