Stability of relative equilibria with singular momentum values in simple mechanical systems

Nonlinearity

Volumn 19, Issue 4, 2006, Pages 853-877

  Rodríguez Olmos, Miguel ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645061774     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/19/4/005     Document Type: Article

References (20)

1. Arnold V I 1966 Sur la géometrie differentielle des groupes de Lie de dimension infinie et ses applications l'hydrodynamique des fluids parfaits Ann. Inst. Fourier, Grenoble 16 319-61
2. Duistermaat J J and Kolk J A C 2000 Lie Groups (Berlin: Springer)
3. Golubitsky M, Stewart I and Schaeffer D G 1988 Singularities and Groups in Bifurcation Theory (Applied Mathematical Sciences vol II) (New York: Springer) p 69
4. Karapetyan A V 1990 The Routh theorem and its extensions Qualitative Theory of Differential Equations (Szeged, 1988) (Colloq. Math. Soc. Janos Bolyai vol 53) (Amsterdam: North-Holland) pp 271-90
5. Lerman E and Singer S F 1998 Stability and persistence of relative equilibria at singular values of the moment map Nonlinearity 11 1637-49
6. Lewis D 1992 Lagrangian block-diagonalization J. Dyn. Diff. Eqns 4 1-41
7. Lewis D 1993 Bifurcations of liquid drops Nonlinearity 6 491-522
8. Lewis D, Ratiu T S, Simo J C and Marsden J E 1992 The heavy top: a geometric treatment Nonlinearity 5 1-48
9. Marsden J E 1992 Lectures on Mechanics (Lecture Note Series vol 174) (Cambridge: Cambridge University Press)
10. Montaldi J 1997 Persistence and stability of relative equilibria Nonlinearity 10 449-66
11. Ortega J-P and Ratiu T S 1999 Stability of Hamiltonian relative equilibria Nonlinearity 12 693-720
12. Palais R S 1961 On the existence of slices for actions of non-compact Lie groups Ann. Math. 73 265-323
13. Paternain G P 1999 Geodesic Flows (Progress in Mathematics vol 180) (Basle: Birkhauser)
14. Pascal M 1975 Sur la recherche des mouvements stationnaires dans les systemes ayant des variables cycliques Celestial Mech. 12 337-58
15. Patrick G W 1992 Relative equilibria in Hamiltonian systems: the dynamic interpretation of nonlinear stability on a reduced phase space J. Geom. Phys. 9 111-19
16. Patrick G W, Roberts M and Wulff C 2002 Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods Arch. Ration. Mech. Anal. 174 301-44 (Preprint math.DS/0201239)
17. Perlmutter M, Rodríguez-Olmos M and Sousa-Dias E 2004 The symplectic normal space of a cotangent-lifted action Preprint math.SG/0501207
18. Routh E J 1877 A Treatise on the Stability of a Given State of Motion (London: MacMillan)
19. Simo J C, Lewis D and Marsden J E 1991 Stability of relative equilibria. Part I: The reduced energy-momentum method Arch. Ration. Mech. Anal. 115 15-59
20. Smale S 1970 Topology and mechanics I Invention. Math. 10 305-31