Methods of Differential Geometry in Analytical Mechanics


  • M. de León
  • P.R. Rodrigues

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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Book information

  • Published: January 1989
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-88017-8


I would assess this being fairly good and would recommend it for providing a nice compilation of much of the recent research in the area.
D.E. Betounes, Mathematical Reviews

Table of Contents

1. Differential Geometry. 2. Almost Tangent Structures and Tangent Bundles. 3. Structures on Manifolds. 4. Connections in Tangent Bundles. 5. Symplectic Manifolds and Cotangent Bundles. 6. Hamiltonian Systems. 7. Lagrangian Systems. 8. Presymplectic Mechanical Systems. Appendices: A Brief Summary of Particle Mechanics in Local Coordinates. Higher Order Tangent Bundles. Generalities. Bibliography. Index.