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.
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机译：Dyson（Am。J. Phys。58（1990）209），Hojman and Shepley（J. Math。Phys。32（1991）142）和Hughes（Am.J. Phys。60（ （1992）142）与我们在切线束（速度相空间）上的泊松括号的定义相结合，以新颖的观点解决牛顿力学中的Noether定理反演和逆问题，而无需假设先验是拉格朗日或哈密顿。从这个角度出发，我们研究了拉格朗日的存在性，唯一性和形式，以及如何将守恒律转变为Noether对称性。
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