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.
Author(s): Manuel de León and Paulo R. Rodrigues (Eds.)
Series: North-Holland Mathematics Studies 158
Publisher: North Holland
Year: 1989
Language: English
Pages: ii-v, 1-483
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
