On the Principle of Stationary Isoenergetic Action
Božidar Jovanović (2012)
Publications de l'Institut Mathématique
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Displaying similar documents to “The degenerate C. Neumann system I: symmetry reduction and convexity”
On the Principle of Stationary Isoenergetic Action
The Lagrange rigid body motion
Tudor Ratiu, P. van Moerbeke (1982)
Annales de l'institut Fourier
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We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group with...
Equivariant normal form for nondegenerate singular orbits of integrable hamiltonian systems
Eva Miranda, Nguyen Tien Zung (2004)
Annales scientifiques de l'École Normale Supérieure
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Symmetries and Integrability
Božidar Jovanović (2008)
Publications de l'Institut Mathématique
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A geometric setting for classical molecular dynamics
Toshihiro Iwai (1987)
Annales de l'I.H.P. Physique théorique
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The geometry of nondegeneracy conditions in completely integrable systems (corrected version of fascicule 4, volume XIV, 2005, p. 705-719)
Nicolas Roy (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using the notion of regular completely integrable systems defined by a fibration of a symplectic manifold by lagrangian tori together with a Hamiltonian function constant on the fibers. In this paper, we give a geometrical definition of different nondegeneracy...
Integrable systems and group actions
Eva Miranda (2014)
Open Mathematics
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The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.