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The complex geometry of Lagrange top

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

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Lubomir Gavrilov, Angel Zhivkov. 1998-09-09. The complex geometry of Lagrange top. https://arxiv.org/abs/solv-int/9809012

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