Descripción: |
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 |