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Fiber derivative, the Glossary

Index Fiber derivative

In the context of Lagrangian mechanics, the fiber derivative is used to convert between the Lagrangian and Hamiltonian forms.[1]

Table of Contents

  1. 5 relations: Cotangent bundle, Hamiltonian mechanics, Lagrangian mechanics, Legendre transformation, Tangent bundle.

  2. Lagrangian mechanics

Cotangent bundle

In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold.

See Fiber derivative and Cotangent bundle

Hamiltonian mechanics

In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833.

See Fiber derivative and Hamiltonian mechanics

Lagrangian mechanics

In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action).

See Fiber derivative and Lagrangian mechanics

Legendre transformation

In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, is an involutive transformation on real-valued functions that are convex on a real variable.

See Fiber derivative and Legendre transformation

Tangent bundle

A tangent bundle is the collection of all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself.

See Fiber derivative and Tangent bundle

See also

Lagrangian mechanics

References

[1] https://en.wikipedia.org/wiki/Fiber_derivative