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Regular classes of linear extensions of dynamical systems on a torus

Morawiak M.

Silesian Journal of Pure and Applied Mathematics

2018

Vol. 8, iss. 1

21--31

The paper presents new methods of construction of the Lyapunov function for some sets of linear extensions of dynamic systems on torus.The paper is divided into two parts. The first part contains a brief theoretical introduction. In the second part are presented results of study and examples.

On regularity of linear systems of differential equations

Morawiak M.

Silesian Journal of Pure and Applied Mathematics

2018

Vol. 8, iss. 1

5--20

The paper presents the theorems about regularity of systems of differential equations. The paper is divided into two parts. The first part contains a theoretical introduction. The second part contains theorems which allows to determine the regularity of the system using the generalized Lyapunov function.

Certain methods of complementation of linear extensions of dynamic systems to regular systems

Kulyk V., Pączko D.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

2014

z. 4

41--55

The paper presents a method of transformation of two weakly regular systems into one regular system. The method has been generalised to any number of weakly regular systems.

W artykule przedstawiono metodę doprowadzenia dwóch układów słabo regularnych do jednego układu regularnego. Metoda została uogólniona na dowolną liczbę układów słabo regularnych.

Drgania własne regularnego układu o "n" stopniach swobody w ujęciu analitycznym

Palej R., Goik T.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

2002

z. 60 [197]

465-472

The paper deals with the free vibrations of damped multi-degree-of-freedom-systems. The criterion of critical damping as well as the total number of damping cases are discussed. The analytical solutions for chosen cases are presented. General considerations have been illustrated by a numerical example where time response of a 50-degree-of-freedom-system to a velocity jump of the end mass is presented.