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arXiv · 1210.4976

The role of integrability in a large class of physical systems

David Delphenich
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Abstract

A large class of physical systems involves the vanishing of a 1-form on a manifold as a constraint on the acceptable states. This means that one is always dealing with the Pfaff problem in those cases. In particular, knowing the degree of integrability of the 1-form is often essential, or, what amounts to the same thing, its canonical (i.e., normal) form. This paper consists of two parts: In the first part, the Pfaff problem is presented and discussed in a largely mathematical way, and in the second part, the mathematical generalities thus introduced are applied to various physical models in which the normal form of a 1-form has already been implicitly introduced, such as non-conservative forces, linear non-holonomic constraints, the theory of vortices and equilibrium thermodynamics. The role of integrability in the conservation of energy is a recurring theme.

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David Delphenich. 2012-10-14. The role of integrability in a large class of physical systems. https://arxiv.org/abs/1210.4976

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