Conserved Quantity - Lagrangian Mechanics

Lagrangian Mechanics

Suppose a system is defined by the Lagrangian L with generalized coordinates q. If L has no explicit time dependence (so ), then the energy E defined by

is conserved.

Furthermore, if, then q is said to be a cyclic coordinate and the generalized momentum p defined by

is conserved. This may be derived by using the Euler-Lagrange equations.

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