  The physical spin program at high $p_T$ region and energies $s^{1/2}_{NN}
\sim 10 GeV$ is discussed. It's shown that cumulative processes, color
transparency problem and polarization phenomenons directly connect with
properties new form of the nuclear matter as Color Quark Condensate(CQC).
Studies of CQC one of the most important physical problem and can be realized
using polarized ion beams at JINR nuclotron-M (and in future at NICA). The
calculations of spin resonance strengthes in the linear approximation for p, d,
t and $^3He$ beams in the JINR nuclotron are presented. The methods to preserve
the degree of polarization during crossing the spin resonances are examined.
The method of matching the direction of polarization vector during the beam
injection in to the ring of the nuclotron is given. These methods of spin
resonance crossing can be used to accelerate polarized beams in the other
cyclic accelerators.
