On a Non-variational Viewpoint in Newtonian Mechanics

Abstract

Certain features of the works of Dyson (Am. J. Phys. 58(1990) 209 ), Hojman and Shepley (J. Math. Phys. 32(1991) 142), and, Hughes (Am.J. Phys. 60(1992) 142 ) are integrated with our definition of the Poisson bracket on a tangent bundle (velocity phase space ) to address the Noether theorem inversion and inverse problem in the Newtonian mechanics from a novel viewpoint without assuming apriori a Lagrangian or Hamiltonian . From this standpoint we study the existence, uniqueness and form of the Lagrangian, and, how to pass from conservation laws to Noether symmetries.

Keywords: Noether theorem, Conservation laws, Symmetry