Abstract
The absolutely new, simple and effective theory is proposed which differs from the classical Liapunov's theory of the movement steadiness. This theory permits to simplify and to speed up the search for the stable movement many times. The classical theory is very complex for using in the engineer practice and one does not bring success in many cases. It was necessary to create a theory that would be devoid of all shortcomings of the classical theory. In this work, it is proposed exactly such theory. Instead of the very complex Liapunov’s function we propose to use the variations calculation. This gives the invaluable winner in the speed and simplicity while searching for the stable movement.
Highlights
Investigations in the sphere of the movement steadiness began in the end of 19 century in several works of E
Result The absolutely new, simple and effective theory is worked out which differs from the classical Liapunov's theory and from all known theories [1,2,3,4,5,6,7,8,9] of the movement steadiness
It was demonstrated on the examples that the proposed new theory of the movement stability is far simpler and more effective than the classic Liapunov's theory and all its known modifications and improvements [1,2,3,4,5,6,7,8,9]
Summary
Investigations in the sphere of the movement steadiness began in the end of 19 century in several works of E. He proposed the general formulation for the stable motion problem. Liapunov's method of the positive-definite functions has remained the most common. Liapunov's method is based on the sufficient conditions of the stable motion. If by means of sufficient conditions it is impossible to solve the problem, it does not mean that the solution does not exist. Whereas by means of the sufficient conditions it often turns out impossible in principle to find the desirable solution for the problem. The classical Liapunov's theory often does not permit to find asymptotical steadiness even if one exists
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