# Difference between revisions of "Lagrangian"

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− | The '''Lagrangian''' of a dynamical system is a function used to describe the dynamics of that system. In classical mechanics, the general definition of the Lagrangian is a function used to describe the difference between the kinetic and potential energies of a dynamical system: | + | The '''Lagrangian''' of a dynamical system is a function used to describe the dynamics of that system. In [[classical mechanics]], the general definition of the Lagrangian is a function used to describe the difference between the kinetic and potential energies of a dynamical system: |

<math>L=T-V</math> | <math>L=T-V</math> | ||

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where <math>T</math> is the [[kinetic energy]] and <math>V</math> is the [[potential energy]]. | where <math>T</math> is the [[kinetic energy]] and <math>V</math> is the [[potential energy]]. | ||

− | The Lagrangian of a system can be used in the [[Euler-Lagrange equation]] in order to derive the equations of motion for the system. | + | The Lagrangian of a system can be used in the [[Lagrangian Dynamics|Euler-Lagrange equation]] in order to derive the equations of motion for the system. |

The general idea behind the Lagrangian is to divorce the dynamical system from any specific coordinate system. | The general idea behind the Lagrangian is to divorce the dynamical system from any specific coordinate system. |

## Revision as of 16:27, 23 November 2016

The **Lagrangian** of a dynamical system is a function used to describe the dynamics of that system. In classical mechanics, the general definition of the Lagrangian is a function used to describe the difference between the kinetic and potential energies of a dynamical system:

where is the kinetic energy and is the potential energy.

The Lagrangian of a system can be used in the Euler-Lagrange equation in order to derive the equations of motion for the system.

The general idea behind the Lagrangian is to divorce the dynamical system from any specific coordinate system.