Euler-type Relative Equilibria and their Stability in Spaces of Constant Curvature
| Autor: | Juan Manuel Sánchez-Cerritos, Ernesto Pérez-Chavela |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Geodesic
General Mathematics 010102 general mathematics Mathematical analysis Space (mathematics) 01 natural sciences Stability (probability) Measure (mathematics) 010305 fluids & plasmas Constant curvature symbols.namesake 0103 physical sciences Euler's formula symbols Algebraic curve 0101 mathematics Curved space Mathematics |
| Zdroj: | Canadian Journal of Mathematics. 70:426-450 |
| ISSN: | 1496-4279 0008-414X |
| Popis: | We consider three point positivemasses moving onS2andH2. An Eulerian-relative equilibrium is a relative equilibrium where the three masses are on the same geodesic. In this paper we analyze the spectral stability of these kind of orbits where the mass at the middle is arbitrary and the masses at the ends are equal and located at the same distance from the central mass. For the case of S2, we found a positive measure set in the set of parameters where the relative equilibria are spectrally stable, and we give a complete classiûcation of the spectral stability of these solutions, in the sense that, except on an algebraic curve in the space of parameters, we can determine if the corresponding relative equilibriumis spectrally stable or unstable. OnH2, in the elliptic case, we prove that generically all Eulerian-relative equilibria are unstable; in the particular degenerate case when the two equal masses are negligible, we get that the corresponding solutions are spectrally stable. For the hyperbolic case we consider the system where the mass in the middle is negligible; in this case the Eulerian-relative equilibria are unstable. |
| Databáze: | OpenAIRE |
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