O ct 2 00 5 Frame - independent mechanics : geometry on affine bundles 1
نویسندگان
چکیده
Main ideas of the differential geometry on affine bundles are presented. Affine counterparts of Lie algebroid and Poisson structures are introduced and discussed. The developed concepts are applied in a frame-independent formulation of the time-dependent and the Newtonian mechanics. MSC (2000): 37J05, 53A40, 53D99, 55R10, 70H99.
منابع مشابه
O ct 2 00 5 Frame - independent mechanics : geometry on affine bundles
Main ideas of the differential geometry on affine bundles are presented. Affine counterparts of Lie algebroid and Poisson structures are introduced and discussed. The developed concepts are applied in a frame-independent formulation of the time-dependent and the Newtonian mechanics. MSC (2000): 37J05, 53A40, 53D99, 55R10, 70H99.
متن کاملFrame-independent formulation of Newtonian mechanics
Based on ideas of W. M. Tulczyjew, a frame independent formulation of analytical mechanics in the Newtonian space-time is presented. The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one dimensional affine bundles replace functions on manifolds, is used. Lagrangian and hamiltonian generating objects, togethe...
متن کاملAV-differential geometry and Newtonian mechanics
A frame independent formulation of analytical mechanics in the Newtonian space-time is presented. The differential geometry of affine values (AV-differential geometry) i.e., the differential geometry in which affine bundles replace vector bundles and sections of one dimensional affine bundles replace functions on manifolds, is used. Lagrangian and hamiltonian generating objects, together with t...
متن کاملAV-differential geometry: Poisson and Jacobi structures
Based on ideas of W. M. Tulczyjew, a geometric framework for a frame-independent formulation of different problems in analytical mechanics is developed. In this approach affine bundles replace vector bundles of the standard description and functions are replaced by sections of certain affine line bundles called AV-bundles. Categorial constructions for affine and special affine bundles as well a...
متن کاملAV-differential geometry: Euler-Lagrange equations
A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and unifies various geometrical approaches to mechanics in the Lagrangian and Hamiltonian pictures, including time-dependent lagrangians and hamiltonians. In our...
متن کامل