en>Bgwhite: WP:CHECKWIKI error fix. Broken bracket problem. Do general fixes and cleanup if needed. - using AWB (9782)

2013-12-17T06:01:20Z

WP:CHECKWIKI error fix. Broken bracket problem. Do general fixes and cleanup if needed. - using AWB (9782)

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{{Orphan|date=February 2013}}

{{unreferenced|date=August 2012}}
In the context of [[Lagrangian Mechanics]] the '''fiber derivative''' is used to convert between the Lagrangian and [[Hamiltonian Mechanics|Hamiltonian]] forms. In particular, if <math>Q</math> is the configuration manifold then the Lagrangian <math>L</math> is defined on the [[tangent bundle]] <math>TQ</math> and the Hamiltonian is defined on the [[cotangent bundle]] <math>T^* Q</math>—the fiber derivative is a map <math>\mathbb{F}L:TQ \rightarrow T^* Q</math> such that

:<math>\mathbb{F}L(v) \cdot w = \frac{d}{ds}|_{s=0} L(v+sw)</math>,

where <math>v</math> and <math>w</math> are vectors from the same tangent space. When restricted to a particular point, the fiber derivative is a [[Legendre transformation]].

[[Category:Lagrangian mechanics]]

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en>Bgwhite: WP:CHECKWIKI error fix. Broken bracket problem. Do general fixes and cleanup if needed. - using AWB (9782)