Definition
In classical mechanics, the natural form of the Lagrangian is defined as the kinetic energy, T, of the system minus its potential energy, V. In symbols,
If the Lagrangian of a system is known, then the equations of motion of the system may be obtained by a direct substitution of the expression for the Lagrangian into the Euler–Lagrange equation. The Lagrangian of a given system is not unique, but solving any equivalent Lagrangians will give the same equations of motion.
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