Abstract
In this paper, we indicate that after the Liapunov function by using linear combination of mechanical first integral was suggested by Chetayev in 1946. He and his students solved stability of conservative system by means of this method. But he had trouble to solve the problems by means of cut and try. Moreover, the condition of stability is imperfect. Solution by this method is limited for problems of purely imaginary roots. The cases of zero roots have not been considered. Condition of stability secured is more strict.
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