Geometric Mechanics

ISBN-13: 9783540442424 / Angielski / Miękka / 2002 / 276 str.

W. M. Oliva; Waldyr M. Oliva

Opis

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, considering Newtonian mechanics, special and general relativity.

Spis treści

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.