Helicity in Hamiltonian dynamical systems

TL;DR

This paper explores the role of helicity as an invariant in Hamiltonian systems, demonstrating how its conservation can impose bounds on other dynamical quantities through illustrative examples.

Contribution

It introduces the concept of helicity within Hamiltonian dynamics and shows its implications for bounding other system properties, a novel perspective in the field.

Findings

Helicity is confirmed as a conserved invariant in Hamiltonian systems.

Conservation of helicity can impose bounds on other dynamical quantities.

Examples illustrate the nontrivial implications of helicity conservation.

Abstract

Helicity plays a unique role as an integral invariant of a dynamical system. In this paper, the concept of helicity in the general setting of Hamiltonian dynamics is discussed. It is shown, through examples, how the conservation of overall helicity can imply a bound on other quantities of the motion in a nontrivial way.