Skip to main content
  • Book
  • © 2002

Geometric Mechanics

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1798)

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (16 chapters)

  1. Front Matter

    Pages N2-XI
  2. Introduction

    • Waldyr Muniz Oliva
    Pages 1-2
  3. 1. Differentiable manifolds

    • Waldyr Muniz Oliva
    Pages 3-12
  4. 3. Pseudo-Riemannian manifolds

    • Waldyr Muniz Oliva
    Pages 23-53
  5. 4. Newtonian mechanics

    • Waldyr Muniz Oliva
    Pages 55-60
  6. 5. Mechanical systems on Riemannian manifolds

    • Waldyr Muniz Oliva
    Pages 61-110
  7. 6. Mechanical systems with non-holonomic constraints

    • Waldyr Muniz Oliva
    Pages 111-126
  8. 8. Special relativity

    • Waldyr Muniz Oliva
    Pages 145-163
  9. 9. General relativity

    • Waldyr Muniz Oliva
    Pages 165-181
  10. A. Hamiltonian and Lagrangian formalisms

    • Waldyr Muniz Oliva
    Pages 183-193
  11. B. Möbius transformations and the Lorentz group

    • Waldyr Muniz Oliva
    Pages 195-221
  12. C. Quasi-Maxwell form of Einstein’s equation

    • Waldyr Muniz Oliva
    Pages 223-244
  13. D. Viscosity solutions and Aubry-Mather theory

    • Waldyr Muniz Oliva
    Pages 245-257
  14. References

    • Waldyr Muniz Oliva
    Pages 259-261
  15. Index

    • Waldyr Muniz Oliva
    Pages 263-270
  16. Back Matter

    Pages 271-276

About this book

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 Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.

Keywords

  • dynamical Systems
  • general relativity
  • geometric mechanics
  • holonomic and non-holonomic systems
  • manifold
  • special relativity

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions