Manifolds and Mechanics

, by Arthur Jones , Alistair Gray , Robert Hutton

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ISBN: 9780521336505 | 0521336503
Cover: Paperback
Copyright: 7/31/1987

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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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Calculus preliminaries
Differential manifolds
Submanifolds
Differentiability
Tangent spaces and maps
Tangent bundles as manifolds
Partial derivatives
Deriving Langrange's equations
Form of Langrange's equations
Vectorfields
Langrangian vectorfields
Flows
The spherical pendulum
Rigid bodies
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Manifolds and Mechanics

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