Abstract
Actual problem of the theory of stability is creation of strict and effective methods of research of the loss of stability of movement of systems with distributed parameters, in particular for continuous environments. This problem has a huge impact on both theoretical and applied uses. In the article is presented the research of the loss of stability of the equations which describe mathematical models of soil massifs and the bases. These models reflect the character of the soil under load, are based on the laws of structural mechanics and the theory of elasticity. The adjoin method offered by Kudinov A.N. was applied to research of the loss of stability. The main advantage of the adjoin method is that for use to the problems of dynamic stability studies in various fields of science and technology, if their equations can be reduced to the equations of second order, don’t demand the introduction of Lyapunov functions. The developed algorithm allows to find positions of balance of the decision and to check up stability of system by adjoin method. The research of stability of the solution of linear systems by using Lyapunov’s method of first approximation is presented in the article.
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