The Complex Geometry of Lagrange Top
نویسنده
چکیده
Abstract We prove that the heavy symmetric top (Lagrange, 1788) linearizes on a two–dimensional non– compact algebraic group – the generalized Jacobian of an elliptic curve with two points identified. This leads to a transparent description of its complex and real invariant level sets. We deduce, by making use of a Baker–Akhiezer function, simple explicit formulae for the general solution of the Lagrange top. At last we describe the two real structures of the Lagrange top and their relation with the focusing and the non–focusing non–linear Schrödinger equation.
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