Geometric Mechanics

• Main Author: Oliva, Waldyr Muniz (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1798
• Subjects: Mathematical physics.; Dynamics.; Ergodic theory.; Theoretical, Mathematical and Computational Physics.; Dynamical Systems and Ergodic Theory.

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 Mechanic...

Table of Contents:

• Introduction
• 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.