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Fiber derivative : ウィキペディア英語版
Fiber derivative

In the context of Lagrangian Mechanics the fiber derivative is used to convert between the Lagrangian and Hamiltonian forms. In particular, if Q is the configuration manifold then the Lagrangian L is defined on the tangent bundle TQ and the Hamiltonian is defined on the cotangent bundle T^
* Q—the fiber derivative is a map \mathbbL:TQ \rightarrow T^
* Q such that
:\mathbbL(v) \cdot w = \frac|_ L(v+sw),
where v and w are vectors from the same tangent space. When restricted to a particular point, the fiber derivative is a Legendre transformation.



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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