General Volume-Preserving Mechanical Systems.

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold (<MATH>{\cal M}</MATH>,ω) via the highest Euler–Lagrange cohomology. It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in Hamilton mechanics. The ordinary canonical equations are included as a special case with a 2-form 1/(n - 1)Hω, where H is the corresponding Hamiltonian. [ABSTRACT FROM AUTHOR]