Manchester Applied Mathematics and Numerical Analysis Seminars
Lecture Theatre OF/B9 Oddfellows Hall (Material Science)
We consider two bodies, any two points of which interact with a given law depending on the distance between these points and their masses, or charge (or some other measure). We suppose that the size of the bodies is much less than the distance between them. We obtain formulae for the potential energy of interaction of these bodies in terms of an asymptotical series. This expression can be used for consideration of celestial mechanics problems, as well as for modelling of particle interaction of a different nature. We pay special attention to the moment interaction of bodies. The case of gravitational interaction is considered in detail. We obtain concrete expressions for a gravitational moment acting upon a rigid body. The first approximation for the problem of two gravitationally interacting bodies is the problem of a rigid body in a Newtonian field of force. We consider this problem for a body with rotational symmetry fixed in the centre of mass. The regimes of regular precession are found and their stability is investigated. Another problem we consider is the rotational motion of an infinite system of rigid bodies fixed at their centres of mass in the points of a cubic lattice. It is assumed that every body interacts gravitationally with its six neighbours. We go from consideration of a discrete system to a polar continuum. We show that the regime of rotation around one of the lattice axes is unstable.
For further info contact either Matthias Heil (email@example.com), Mark Muldoon (M.Muldoon@umist.ac.uk) or the seminar secretary (Tel. 0161 275 5800).