# James Montaldi - The 2-body problem on surfaces of constant curvature

Dates: | 24 October 2019 |
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Times: | 14:30 - 15:30 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Speaker: | James Montaldi |

James Montaldi joins us for the Geometry, Topology and Mathematicals Physics Seminar.

Abstract:

By reducing to the centre of mass frame, the 2-body problem in the plane reduces to the Kepler problem (1 body in a central force). On a curved surface, there is no useful centre of mass frame, and the 2-body problem does not reduce to such a simpler system. In this talk I will describe the process of reduction one can do, and the relative equilibria of this system of 2 bodies on surfaces of constant curvature. I will also describe how the relative equilibria for positive curvature and for negative curvature fit into a family through zero curvature (spherical/planar/hyperbolic geometries).

This is joint work with A. Borisov, I. Mamaev, and in particular Luis GarcĂa-Naranjo.

### Speaker

James Montaldi