On a class of three dimensional quadratic Hamiltonian systems

TL;DR

This paper computes the normal form of a broad class of three-dimensional quadratic Hamiltonian systems, extending Euler's equations from rigid body dynamics to a more general framework.

Contribution

It introduces a generalized class of quadratic Hamiltonian systems and derives their normal forms, expanding the understanding of such systems beyond classical rigid body models.

Findings

Derived the normal form for the class of systems

Extended Euler's equations to a broader context

Provided mathematical tools for analyzing quadratic Hamiltonian systems

Abstract

The purpose of this article is to compute the normal form of a class of general quadratic Hamiltonian systems that generalizes naturally Euler's equations from the free rigid body dynamics.