Department of Mathematics, Chaohu College, Chaohu 238000, China; Department of Physics, Chaohu College, Chaohu \rm 238000, China
Abstract:
This paper extends Hojman's conservation law to the third-order
differential equation. A new conserved quantity is constructed based
on the Lie group of transformation generators of the equations of
motion. The generators contain variations of the time and
generalized coordinates. Two independent non-trivial conserved
quantities of the third-order ordinary differential equation are
obtained. A simple example is presented to illustrate the
applications of the results.