# On Time-dependent Hamiltonian Realizations of Planar and Nonplanar Systems

## TL;DR

This paper explores the use of cosymplectic geometry to generalize time-dependent Hamiltonian systems, including Nambu-Poisson structures, providing new mathematical frameworks and illustrative examples.

## Contribution

It introduces a generalization of cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and develops a Jacobi last multiplier for 3D cases.

## Key findings

- Generalized cosymplectic structures to Nambu-Poisson systems
- Developed Jacobi last multiplier for 3D systems
- Provided illustrative examples of the new frameworks

## Abstract

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems. In particular, we generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3D systems. We illustrate our constructions with various examples.