Euler top and freedom in supersymmetrization of one-dimensional mechanics

Abstract

In this paper we formulate the Euler top as a system on the complex projective plane, playing the role of phase space, i.e., as a one-dimensional mechanical system. Then we suggest the supersymmetrization scheme of the generic one-dimensional systems with positive Hamiltonian which yields á priori integrable family of N=2k supersymmetric Hamiltonians parameterized by N/2 arbitrary real functions.