Generalizing the classical fixed-centres problem in a non-Hamiltonian way
| Autor: | A Albouy, T J Stuchi |
|---|---|
| Přispěvatelé: | Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Astronomie et systèmes dynamiques (ASD), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Instituto de Física, Universidade Federal do Rio Grande do Sul |
| Rok vydání: | 2004 |
| Předmět: |
Integrable system
Generalization Mathematical analysis General Physics and Astronomy Statistical and Nonlinear Physics Numerical integration Mathematical Operators Gravitation symbols.namesake Bounded function Euler's formula symbols [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph] Hamiltonian (quantum mechanics) Mathematical Physics Mathematics Mathematical physics |
| Zdroj: | Journal of Physics A: Mathematical and General (1975-2006) Journal of Physics A: Mathematical and General (1975-2006), 2004, 37, pp.9109-9123. ⟨10.1088/0305-4470/37/39/005⟩ |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/37/39/005 |
| Popis: | International audience; The problem of two gravitational (or Coulombian) fixed centres is a classical integrable problem, stated and integrated by Euler in 1760. The integrability is due to the unexpected first integral G. We introduce some straightforward generalizations of the problem that still have the generalization of G as a first integral, but do not possess the energy integral. We present some numerical integrations showing the main features of their dynamics. In the domain of bounded orbits the behaviour of these a priori non-Hamiltonian systems is very similar to the behaviour of usual near-integrable systems. |
| Databáze: | OpenAIRE |
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