The Fundamental Analytic Theorems of the Inverse Problem

Abstract

We consider now the conventional analytic equations¹ in configuration space, i.e., Lagrange’s equations:

$$ \eqalign{ & {L_k}(q) = \frac{d}{{dt}}\frac{{\partial L(t,q,\dot q)}}{{\partial {{\dot q}^k}}} - \frac{{\partial L(t,q,\dot q)}}{{\partial {q^k}}} = 0, \cr & {\text{ k = 1,2,}} \ldots {\text{,n}}{\text{.}} \cr} $$

((3.1.1))

Our problem is to identify the necessary and sufficient conditions for regular holonomic Newtonian systems in their fundamental form (2.2.1) to admit a representation in terms of Equations (3.1.1).