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arXiv · 2504.16701

Spinning top in quadratic potential and matrix dressing chain

V. E. Adler·A. P. Veselov
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Abstract

We show that the equations of motion of the rigid body about centre of mass in the Newtonian field with a quadratic potential are special reductions of period-one closure of the Darboux dressing chain for the Schrödinger operators with matrix potentials. We show that the corresponding matrix Schrödinger operators are maximally finite-gap (in the sense that for all sufficiently large energies all solutions of the corresponding Schrödinger equation are bounded) and describe their spectrum explicitly. The general $2\times 2$-matrix case of the dressing chain, providing also some exotic matrix versions of the harmonic oscillator, is discussed in more detail.

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V. E. Adler, A. P. Veselov. 2026-03-14. Spinning top in quadratic potential and matrix dressing chain. https://doi.org/10.1134/s1560354725040021

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