Kowalevski integal on Lie groups and addition formulas for elliptic curves

Velimir Jurdjevic, University of Toronto

The equations of the spinning top are particular cases of left invariant optimal control problems on Lie groups. These connections illuminate the integrable cases of the spinning top. I will show these connectons and concentrate on the Kowalevski case. It turns out that the integration procedure of the original work of Kowalevska extends to this more general situation, and its proper geometric interpretation clarifies the paper of Euler of 1765, and a paper of Weil of 1954 concerning the group structure of elliptic curves.