Aly, J. J. On the lowest energy state of a collisionless self-gravitating system under phase space volume constraints. (English) Zbl 0682.70009 Mon. Not. R. Astron. Soc. 241, No. 1, 15-27 (1989). Summary: The problem of minimizing the energy of a collisionless self-gravitating system under the only constraint of phase space volume conservation is reconsidered. We bring about essentially three new results: (i) we establish a lower bound on the energy by using arguments which are both simpler and more general than those of other authors; (ii) we prove that the lowest energy state is necessarily spherically symmetric (in the physical space), and (iii) we show that, if we fix also the total angular momentum J of the system, then there is no lowest energy state satisfying this further constraint if \(J\neq 0\). Cited in 2 ReviewsCited in 8 Documents MSC: 70F10 \(n\)-body problems 70F15 Celestial mechanics 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics Keywords:minimizing the energy; collisionless self-gravitating system; constraint of phase space volume conservation; lower bound on the energy; lowest energy state PDFBibTeX XMLCite \textit{J. J. Aly}, Mon. Not. R. Astron. Soc. 241, No. 1, 15--27 (1989; Zbl 0682.70009) Full Text: DOI