Stability preserving structural transformations of systems of linear second-order ordinary differential equations

Details Stability preserving structural transformations of systems of linear second-order ordinary differential equations Stability preserving structural transformations of systems of linear second-order ordinary differential equations

2012-04-09

arxiv.org/abs/1204.1814v1

Mathematics

Dynamical Systems

40 pages

Scientific paper

In the paper we have developed a theory of stability preserving structural transformations of systems of second-order ordinary differential equations (ODEs), i.e., the transformations which preserve the property of Lyapunov stability. The main Theorem proved in the paper can be viewed as an analogous of the Erugin's theorem for the systems of second-order ODEs. The Theorem allowed us to generalize the 3-rd and 4-th Kelvin -- Tait -- Chetayev theorems. The obtained theoretical results were successfully applied to the stability investigation of the rotary motion of a rigid body suspended on a string.

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