Events at The University of Manchester
  • University home
  • Events
  • Home
  • Exhibitions
  • Conferences
  • Lectures and seminars
  • Performances
  • Events for prospective students
  • Sustainability events
  • Family events
  • All Events

Philip Arathoon - Singular reduction of the 2-body problem on the 3-sphere and the 4-dimensional Lagrange top

Dates:5 December 2019
Times:15:00 - 16:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Current University students
Speaker:Philip Arathoon
See travel and contact information
Add to your calendar

Other events

  • In category "Seminar"
  • In group "(Maths) Maths seminar series"
  • In group "(Maths) Geometry, topology and mathematical physics"
  • By Department of Mathematics

Title: Singular reduction of the 2-body problem on the 3-sphere and the 4-dimensional Lagrange top

Abstract:

For the motion of two attracting bodies in Euclidean space, the translational symmetry reduces the system to that of the usual Kepler problem. For two bodies on a sphere this is no longer the case as no such group of translational symmetries exist—except for when the sphere in question is the 3-sphere. In this case, both left and right translations act as symmetries, and together generate the action of SO(4). Furthermore, owing to the double cover of SO(4), the dynamics for the 2-body problem on the sphere double cover the dynamics of a symmetric heavy top in 4 dimensions. The top is a generalised Lagrange top possessing an axis of symmetry within the body. The left and right SO(3) reductions, about the line of gravity and the line of symmetry in the top, correspond under the double cover to the left and right translations of the 2-body problem. We investigate the geometry of the reduced manifolds and study their relative equilibria.

Speaker

Philip Arathoon

Travel and Contact Information

Find event

Frank Adams Room 1
Alan Turing Building
Manchester

Contact event

Theodore Voronov

theodore.voronov@manchester.ac.uk

Contact us

  • +44 (0) 161 306 6000

Find us

The University of Manchester
Oxford Rd
Manchester
M13 9PL
UK

Connect with the University

  • Facebook page for The University of Manchester
  • X (formerly Twitter) page for The University of Manchester
  • YouTube page for The University of Manchester
  • Instagram page for The University of Manchester
  • TikTok page for The University of Manchester
  • LinkedIn page for The University of Manchester

  • Privacy /
  • Copyright notice /
  • Accessibility /
  • Freedom of information /
  • Charitable status /
  • Royal Charter Number: RC000797
  • Close menu
  • Home
    • Featured events
    • Today's events
    • The Whitworth events
    • Manchester Museum events
    • Jodrell Bank Discovery Centre events
    • Martin Harris Centre events
    • The John Rylands Library events
    • Exhibitions
    • Conferences
    • Lectures and seminars
    • Performances
    • Events for prospective students
    • Sustainability events
    • Family events
    • All events