  We describe a new type of top, the twisted top, obtained by appending a
cocycle to the Lie-Poisson bracket for the charged heavy top, thus breaking its
semidirect product structure. The twisted top has an integrable case that
corresponds to the Lagrange (symmetric) top. We give a canonical description of
the twisted top in terms of Euler angles. We also show by a numerical
calculation of the largest Lyapunov exponent that the Kovalevskaya case of the
twisted top is chaotic.
