Abstract:
We show that the equations of motion of a rigid body about a fixed point in
the Newtonian field with a quadratic potential are special reduction of period-one closure of
the Darboux dressing chain for the Schrödinger operators with matrix potentials. Some new
explicit solutions of the corresponding matrix system and the spectral properties of the related
Schr¨odinger operators are discussed.
Keywords:rigid body dynamics, matrix Schrödinger operators, Darboux transformations
