Manifolds and Mechanics

by Arthur Jones, Alistair Gray, Robert Hutton

Overview

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.

Product Details

ISBN-13:	9780521336505
Publisher:	Cambridge University Press
Publication date:	05/14/1987
Series:	Australian Mathematical Society Lecture Series , #2
Pages:	176
Product dimensions:	5.98(w) x 9.02(h) x 0.39(d)

Table of Contents

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.