Nambu mechanics

Summary

Nambu mechanics is a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. In it the motion is driven by two or more Hamiltonians instead of one. The Poisson bracket of two functions is replaced by a bracket of three or more functions, such as the Jacobian determinant on $\R^3$. All the Hamiltonians are conserved, and the flow preserves volume, as in Liouville's theorem. The free rigid body is the standard example. Its equations of motion have this form, with energy and squared angular momentum as the two Hamiltonians. See the definition.