| 摘 要： | In this paper. we indicate that after the Liapunov function by using linear combinationof mechanical first integral was suggested by Chetayev in 1946.He and his students solvedstability of conservative system by means of this method. But he had trouble to solve theproblems 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 zeroroots have not been considered Condition of stability secured is more strict.This paper suggests that the differential equation can be transformed into standardform by method of cancellation of cyclic coordinates(method of lowering degree of order),and condition of stability can be determined by energy integral.By this method not only thecomputation is clear and concise.But also zero roots can be considered.Therefore theproblems of two cyclic coordinates can be transformed into second-order system,and we getnew conclusion of the condition of stability simply .As for problem
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