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The structural influence of the forces of the stability of dynamical systems. (English) Zbl 1199.37010

Summary: We consider the autonomous dynamical system linear or linearized with 2 degrees of freedom. In the system of equations of 4th degree, the structure generalized forces appear: \(K(q)\) - the conservative forces, \(N(q)\) - the non-conservative forces, \(D(\dot q)\) the dissipative forces, \(G(\dot q)\) the gyroscopically forces. In the linear system, these forces from the different structural combinations can produce the stability or the instability of the null solution. The theorems of Thomson - Tait - Cetaev (T-T-C) are known for the configurations \((K, D, G)\). We introduce the non - conservative forces \(N\), studying the stability with the Routh - Hurwitz criterion or constructing the Lyapunov function, obtaining some theorems with practical applications.

MSC:

37A60 Dynamical aspects of statistical mechanics
34D20 Stability of solutions to ordinary differential equations
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
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