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Geometric mechanics /

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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...

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Bibliographic Details
Main Author: Oliva, Waldyr M.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer, [2002]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1798.
Subjects:
Mechanics, Analytic.
Geometry, Differential.
Electronic books.
Online Access:Connect to the full text of this electronic book
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: Mbius transformations and the Lorentz group
  • Appendix C: Quasi-Maxwell equations
  • Appendix D: Viscosity solutions and Aubry-Mather theory.