Manifolds and mechanics
著者
書誌事項
Manifolds and mechanics
（Australian Mathematical Society lecture series, 2）
Cambridge University Press, 1987
- : hard covers
- : pbk
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注記
Includes index
内容説明・目次
内容説明
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.
目次
- 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.
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