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.
Read more about this topic: Conserved Quantity
Famous quotes containing the word mechanics:
“It is only the impossible that is possible for God. He has given over the possible to the mechanics of matter and the autonomy of his creatures.”
—Simone Weil (1909–1943)