The complex geometry of Lagrange top

Details The complex geometry of Lagrange top The complex geometry of Lagrange top

1998-09-09

arxiv.org/abs/solv-int/9809012v1

L'Enseignement Mathematique, tome 44 (1998) p.133-170

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTex, 26 pages

Scientific paper

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 also deduce, by making use of a Baker-Akhiezer function, simple explicit formulae for the general solution of Lagrange top.

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