Manifolds and Mechanics

This book provides an easy introduction to the theory of differentiable manifolds.

Arthur Jones (Author), Alistair Gray (Author), Robert Hutton (Author)

9780521336505, Cambridge University Press

Paperback, published 14 May 1987

176 pages
22.9 x 15.2 x 1 cm, 0.27 kg

This book provides an easy introduction to the theory of differentiable manifolds. The authors then show how the theory can be used to develop, simply but rigorously, the theory of Lanrangian mechanics directly from Newton's laws. Unnecessary abstraction has been avoided to produce an account suitable for students in mathematics or physics who have taken courses in advanced calculus.

1. Calculus preliminaries
2. Differential manifolds
3. Submanifolds
4. Differentiability
5. Tangent spaces and maps
6. Tangent bundles as manifolds
7. Partial derivatives
8. Deriving Langrange's equations
9. Form of Langrange's equations
10. Vectorfields
11. Langrangian vectorfields
12. Flows
13. The spherical pendulum
14. Rigid bodies.

Subject Areas: Applied mathematics [PBW]