Abstract
Assuming that m zero roots correspond to the non-isolated singular point of the equations of disturbed motion, the problem of stability when some of the remaining roots are pure imaginary, while others have a negative real part in inessentially singular cases, is considered. This situation is typical for non-holonomic systems. The stability and instability theorems obtained are used to study the stability of the rotations of a celtic stone on the boundary of the domain of stability.
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