Involution and Constrained Dynamics III: Intrinsic Degrees of Freedom Count

Reference: Technische Mechanik, 20 (2000) 137-146

Description: This paper clarifies some points concerning the degrees of freedom count in constrained systems. The formula given in [8] for the number of degrees of freedom for finite-dimensional systems with gauge symmetries is not always correct (more precisely, it gives wrong results, if secondary first class constraints exist). In this article I present a conceptually much easier approach via Lie pseudogroups that avoids this problem. As a by-product I show how the Hilbert polynomials of two differential equations connected by a differential relation (a very general form of a Bäcklund transformation) are related.

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