Noncanonical Hamiltonian mechanics

A number of books and papers contain the best formulations of noncanonical Hamiltonian mechanics. Here, instead, the object is to present the essential ideas in their most simple‐minded form. The root idea is that quantities are ’’real’’ if they are independent of the coordinate system used to describe them. In orthodox Hamiltonian mechanics a restricted set of coordinate systems is used and interesting quantities are invariant under the canonical transformations that relate these coordinates. Here more general coordinate system will be used, with a reality condition taken from tensor calculus.