Difference between revisions of "Lagrangian"
(New page: The '''Lagrangian''' of a physical system is defined to be <math>L=T-V</math> where <math>T</math> is the kinetic energy and <math>V</math> is the potential energy. == See Also == [[Ham...) |
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| − | The '''Lagrangian''' of a | + | 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> | ||
| − | 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 [[Lagrangian Dynamics|Euler-Lagrange equation]] in order to derive the equations of motion for the system. | |
| − | [[ | ||
| − | [[Category: | + | The general idea behind the Lagrangian is to divorce the dynamical system from any specific coordinate system. |
| + | |||
| + | == See also == | ||
| + | *[[Hamiltonian]] | ||
| + | |||
| + | [[Category:Mechanics]] | ||
Latest revision as of 12:48, April 6, 2017
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.