Merry-go-round and time-dependent symplectic forms

TL;DR

This paper explores how to incorporate the Euler fictitious force in symplectic geometry by using time-dependent symplectic forms and primitives, extending the modeling of fictitious forces in rotating frames.

Contribution

It introduces a method to handle the Euler force symplectically through time-dependent symplectic forms and primitives, expanding the geometric framework for fictitious forces.

Findings

Euler force can be modeled using time-dependent symplectic forms

Time-dependent primitives are necessary for a complete symplectic treatment

Extends symplectic modeling to accelerated rotating frames

Abstract

In the merry-go-round fictitious forces are acting like centrifugal force and Coriolis force. Like the Lorentz force Coriolis force is velocity dependent and, following Arnold, can be modeled by twisting the symplectic form. If the merry-go-round is accelerated an additional fictitious force shows up, the Euler force. In this article we explain how one deals symplectically with the Euler force by considering time-dependent symplectic forms. It will turn out that to treat the Euler force one also needs time-dependent primitives of the time-dependent symplectic forms.