All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 7

Displaying 121 – 135 of 135

Showing per page

The geometry of Calogero-Moser systems

Jacques Hurtubise, Thomas Nevins (2005)

Annales de l’institut Fourier

We give a geometric construction of the phase space of the elliptic Calogero-Moser system for arbitrary root systems, as a space of Weyl invariant pairs (bundles, Higgs fields) on the r -th power of the elliptic curve, where r is the rank of the root system. The Poisson structure and the Hamiltonians of the integrable system are given natural constructions. We also exhibit a curious duality between the spectral varieties for the system associated to a root system, and the Lagrangian varieties for...

The geometry of Newton's law and rigid systems

Marco Modugno, Raffaele Vitolo (2007)

Archivum Mathematicum

We start by formulating geometrically the Newton’s law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. For constrained systems we have intrinsic and extrinsic viewpoints, with respect to the environmental space. Multi–particle systems are modelled on n -th products of the pattern model. We apply the above scheme to discrete rigid systems. We study the splitting of the tangent and cotangent environmental space into the three components of center...

The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles

Charles-Michel Marle (2007)

Banach Center Publications

Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers, Élie Cartan...

Currently displaying 121 – 135 of 135

Previous Page 7