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:
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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:
  
 
<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.
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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.

See also