Fundamental matrix solutions of piecewise smooth differential systems
This paper is concerned with the study of some properties of the matrix solutions of variational equations around continuous solutions of piecewise smooth differential systems. The systems under consideration are termed as Filippov type systems in which the vector field has a finite number of switching surfaces \( \Sigma_j\), \(j=1, \dots ,k\) of discontinuity so that any trajectory that reaches a switching surface \( \Sigma_j\) may be continued either by a transversal intersection or else be continued sliding along \( \Sigma_j\). In the first part of the paper a brief review of Filippov's theory on non smooth differential systems is given. After that a detailed study of the properties of the fundamental matrix solution around a given Filippov solution is carried out both in cross and slide motion on a surface \( \Sigma_j\). Then the theory is extended to the case of two surfaces. The paper ends by illustrating the theory with an example due to \textit{U. Galvanetto} [Journal of Sound and Vibration 248, 653--669 (2001)] which consist of a system of two blocks on a moving belt connected by a spring and subject to a dry friction force, by computing the eigenvalues of the fundamental matrix around a periodic solution.
variational equations around Filippov solutions
properties of fundamental matrix solutions
scientific article; zbMATH DE number 5869213
scientific article