Root
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Conference Proceedings
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5th International Conference on Physics and Control (PhysCon 2011)
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On problem of stability with respect to a part of the variables
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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.

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.