Sydney Dynamics Group: David Pfefferle -- Spinning tops and magneto-hydrodynamics: Part 2

Dear all, 

This week, Friday August 21, David Pfefferle (UWA) will give a talk at 4pm (Sydney
time) via Zoom.  
Zoom link: https://uni-sydney.zoom.us/j/97078333625 
Meeting ID: 970 7833 3625 

Title: Spinning tops and magneto-hydrodynamics: Part 2 

Abstract: 
In part 1, we reviewed the constrained variational problem originating from the
Euler-Poincare reduction of geodesics on Lie groups with left-invariant Riemannan
metric and applied it to the case of SO(3) to derive the well-known Euler equations of a
free rigid body.  In this talk, we replicate those steps in the case of a semidirect
product between the Lie-Frechet group of diffeomorphisms and the space of one-forms on
a domain of real space.  Working at a formal level, this infinite dimensional group is
equipped with a right-invariant Riemannian metric, and out come incompressible ideal
magneto-hydrodynamics equations from the Euler-Poincare reduction.  Rather elegantly,
Alfven’s frozen-in flux theorem is seen as a consequence of the semidirect product
structure (which encodes advection), and relabelling symmetry is attributable to
right-invariance.  

Link to Part 1: https://youtu.be/_TNWDtOIGcQ 

Past talks can be found on the YouTube channel:
https://www.youtube.com/channel/UCZqgDJ21wbdzMbeIdealpUg/ 

I hope to see you all online.  

Lachlan