Manifolds and Mechanics

Arthur Jones; Alistair Gray; Robert Hutton

doi:10.1017/CBO9780511569401

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Arthur Jones, Alistair Gray, Robert Hutton

Publisher:: Cambridge University Press
Online publication date:: January 2010
Print publication year:: 1987
Online ISBN:: 9780511569401
DOI:: https://doi.org/10.1017/CBO9780511569401

Subjects:: Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Geometry and Topology
Series:: Australian Mathematical Society Lecture Series (2)

36.99 (GBP)

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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.

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Manifolds and Mechanics

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

PROLOGUE
pp 1-2

1 - CALCULUS PRELIMINARIES
pp 3-15

2 - DIFFERENTIABLE MANIFOLDS
pp 16-27

3 - SUBMANIFOLDS
pp 28-38

4 - DIFFERENTIABILITY
pp 39-43

5 - TANGENT SPACES AND MAPS
pp 44-54

6 - TANGENT BUNDLES AS MANIFOLDS
pp 55-63

7 - PARTIAL DERIVATIVES
pp 64-77

8 - DERIVING LAGRANGE'S EQUATIONS
pp 78-89

9 - FORM OF LAGRANGE'S EQUATIONS
pp 90-97

10 - VECTORFIELDS
pp 98-109

11 - LAGRANGIAN VECTORFIELDS
pp 110-119

12 - FLOWS
pp 120-137

13 - THE SPHERICAL PENDULUM
pp 138-146

14 - RIGID BODIES
pp 147-158

REFERENCES
pp 159-160

INDEX
pp 161-164

SYMBOL TABLE
pp 165-166

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