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equations for the heavy top extend to a larger class of Hamiltonian systems on Lie groups; this paper explains these extensions, and along the way reveals further geometric significance of her work in the theory of elliptic curves. Specifically, in this paper we shall be concerned with the solutions of the following differential system in six variables hi, h2, h3, H1, H2, H3 dH 1 H2H( d1 = H2H3 - -h- + 23- ha2 , dt C3 C2

Integrable Hamiltonian Systems on Lie Groups: Kowalewski Type