Methods of Differential Geometry in Analytical Mechanics

Manuel de León and Paulo R. Rodrigues (Eds.)0444880178, 9780444880178, 9780080872698

The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint. Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories. The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

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Table of contents :
Content:
Editor
Page ii

Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages 1-2

Chapter 1 Differential Geometry
Pages 3-110

Chapter 2 Almost Tangent Structures and Tangent Bundles
Pages 111-145

Chapter 3 Structures on Manifolds
Pages 147-180

Chapter 4 Connections in Tangent Bundles
Pages 181-225

Chapter 5 Symplectic Manifolds and Cotangent Bundles
Pages 227-262

Chapter 6 Hamiltonian Systems
Pages 263-299

Chapter 7 Lagrangian Systems
Pages 301-397

Chapter 8 Presymplectic Mechanical Systems
Pages 399-438

Appendix A A Brief Summary of Particle Mechanics in Local Coordinates
Pages 439-450

Appendix B Higher Order Tangent Bundles. Generalities
Pages 451-456

Bibliography
Pages 457-469

Index
Pages 471-483