On the reduced phase space of a cotangent bundle

The geometric prequantization of a reduced phase space of a cotangent bundle is described and its relation with the geometric prequantization of the cotangent bundle is pointed out.     

Generalized mechanical systems. A mathematical exposition of non-smooth classical Lagrangian mechanics

In this note we shall give a generalization of classical mechanical systems.     

On the geometric prequantization of Maxwell equations

The geometric prequantization of Maxwell equations in a vacuum is described and its relation with geometric prequantization of the extended phase space is pointed out.     

Geometric quantization of the heavy top

The geometric quantization of the heavy top is described and its relation with the geometric quantization of the cotangent bundle of the orthogonal group is pointed out.     

KAHAN'S INTEGRATOR AND THE FREE RIGID BODYDYNAMICS

1.IntroductionAmongotherunconventionalnumericalmethods,Kahanll]hassuggestedadiscretizationofasimpleLotka-Volterasystemwiththepropertythatthecomputed.pointsdonotspiral.ThemotivationofthisbehaviourwasgivenrecentlybySanzSerna[3]byshowingthatKahan'sintegratorisasymplecticone.Thegoalofourpaperistostudysomepropertiesofthisintegratorintheparticularcaseofthefreerigidbody.2.TheFreeRigidBodyLetSO(3)betheLiegroupofall3x3orthogonalmatriceswithdeterminantoneandso(3)itsLiealgebra.Itcanbecanonicallyide…     

Some remarks on the Clebsch's system

The almost Hamilton-Poisson realization, the stability problem, the existence of periodic solutions and the numerical integration via the Lie-Trotter integrator for the Clebsch system are discussed and some of their properties are pointed out.     

Sur les courants d'une variété différentielle invariants sous l'action d'un groupe de Lie

Sans résumé

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The article is the text of a talk given at the Symposium on Differential Geometry in Debrecen, Hungary, on August 28–September 3, 1975.     

On the geometric prequantization of Poisson manifolds

The geometric prequantization of Poisson manifolds is described using the Weinstein theory of local symplectic groupoids.