Structural transformations of non-conservative systems (Q2761362)

The author studies the matrix equation of the form NEWLINE\[NEWLINE J\ddot x+(D+HG)\dot x+(\Pi+P)x = X(x,\dot x),NEWLINE\]NEWLINE where \(\,x\in \mathbb{R}^n\), \(\,J=J^T\), \(\,D=D^T\), \(\,G=-G^T\), \(\,\Pi=\Pi^T\), \(\,P=-P^T\,\) are \(n\times n\) constant matrices and \(X\) is \(n\)-dimensional vector containing \(x\) and \(\dot x\) in power higher than the first one. Using the transformation technique from [\textit{V.~N.~Koshlyakov}, Ukr. Mat. Zhurn. 49, No. 4, 535-539 (1997; Zbl 0912.70006); Prikl. Mat. Mekh. 61, No. 5, 774--780 (1997; Zbl 0911.70008)], an example of the corrected gyroscopic system and one-rotor corrected gyrocompass are constructed.