On problem of stability with respect to a part of the variables
Julia G. Martyshenko, Vladimir I. Vorotnikov
A stability problem with respect to a part of variables
of the zero equilibrium position is considered for nonlinear
non-stationary systems of ordinary differential
equations with the continuous right-hand side. As compared
to known assumptions, more general assumptions
are made on the initial values of variables noncontrolled
in the course of studying stability. Conditions
of stability and asymptotic stability of this type
are obtained within the method of Lyapunov functions
and generalize a number of existing results. The results
are applied to the stability problem with respect to a
part of variables of equilibrium positions of nonlinear
holonomic mechanical systems.