Viazminsky, Caesar P
January 3, 2018
/Research Papers-Mathematical Physics/Download/7168
We discuss Noether’s theorem [1-7] confined to mechanical systems and show that a symmetry of a system must already be a symmetry of the space. This provides a framework within which one may seek conserved quantities pertaining to a system out of those pertaining to the space. The symmetries of a system are dictated by its potential energy. It is shown that a momentum operator arising from an infinitesimal motion of the space, or a Killing vector field, is conserved if the directional derivative of the potential energy by this Killing vector field vanishes.
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