Direct Hamiltonization for Nambu Systems

TL;DR

This paper demonstrates that Nambu systems can be directly transformed into traditional Hamiltonian systems, showing that Nambu mechanics is a special case of standard Hamiltonian mechanics, and establishes that any system with a specific form is a Nambu system.

Contribution

It introduces a direct hamiltonization method for Nambu systems, revealing their equivalence to standard Hamiltonian mechanics and characterizing all systems of a certain form as Nambu systems.

Findings

Nambu mechanics can be represented as standard Hamiltonian mechanics.

Any system with the form d{f r}/dt={f A(r)} is a Nambu system.

Nambu systems are a particular case of usual Hamiltonian systems.

Abstract

The direct hamiltonization procedure applied to Nambu mechanical systems proves that the Nambu mechanics is an usual mechanics described by only one Hamiltonian. Thus a particular case of Hamiltonian mechanics. It is also proved that any mechanical system described by the equation d{\bf r}/dt={\bf A(r)} is a Nambu system.