Geometric Mechanics

Lecture Notes in Mathematics

Waldyr Muniz Oliva

280 pages, parution le 18/11/2002

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Résumé

Geometric Mechanics here means mechanics on a pseudo-Riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.

Contents

Differentiable manifolds
Vector fields, differential forms and tensor fields
Pseudo-Riemannian manifolds
Newtonian mechanics
Mechanical systems on Riemannian manifolds
Mechanical Systems with non-holonomic constraints
Hyperbolicity and Anosov systems Vakonomic mechanics
Special relativity
General relativity

Appendix A: Hamiltonian and Lagrangian formalism
Appendix B: Möbius transformations and the Lorentz group
Appendix C: Quasi-Maxwell equations
Appendix D: Viscosity solutions and Aubry-Mather theory

L'auteur - Waldyr Muniz Oliva

Instituto Superior Tecnico, Lisbon, Portugal

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Waldyr Muniz Oliva
Parution	18/11/2002
Nb. de pages	280
Format	15,5 x 23,5
Couverture	Broché
Poids	438g
Intérieur	Noir et Blanc
EAN13	9783540442424