Solutions homoclinic to regular precessions of a symmetric satellite

Maciejewski, Andrzej J.; Goźiewski, Krzysztof

doi:10.1007/bf00049515

Cited by 6 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, we note that we have adopted the names of Lagrangian and non-Lagrangian equilibria as Maciejewski suggests in (Maciejewski, 1995). The results obtained here for the two gyrostats problem are similar to the ones obtained by Maciejewski for the two rigid bodies.…”

Section: R = A^r P = A^p R 1 = a I N 1 R 2 = N 2 supporting

confidence: 81%

See 1 more Smart Citation

The Hamiltonian Dynamics of The Two Gyrostats Problem

Mondéjar¹,

Vigueras²

1999

International Astronomical Union Colloquium

View full text Add to dashboard Cite

The problem of two gyrostats in a central force field is considered. We prove that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system posseses symmetries. Using them we perform the reduction of the number of degrees of freedom. We show that at every stage of the reduction process, equations of motion are Hamiltonian and give explicit forms corresponding to non-canonical Poissson brackets. Finally, we study the case where one of the gyrostats has null gyrostatic momentum and we study the zero and the second order approximation, showing that all equilibria are unstable in the zero order approximation.

show abstract

Section: R = A^r P = A^p R 1 = a I N 1 R 2 = N 2 supporting

confidence: 81%

“…The problem of roto-traslatory motion of n-rigid bodies has been studied, amongst other authors by Duboshin (1972), Aboelnaga (1979), Barkin (1980), Wang (1990;1992), and by Maciejewski (1995). They considered the mutual interactions between orbital and rotational motion for artificial and natural bodies in the solar system.…”

Section: Introductionmentioning

confidence: 99%