Integrable extensions of classical elliptic integrable systems

In this article we consider two particular examples of general construction proposed in arXiv:2012.15529. We consider the integrable extensions of the classical elliptic Calogero-Moser model of N particles with spin and the integrable Euler-Arnold top related to the group SL(N,C). The extended systems has additional N-1 degrees of freedom and can be described in terms of the Darboux variables.
Comment: 14 pages. Contribution in the TMP volume dedicated to the ninetieth anniversary of M.K. Polivanov's birth