A qualitative analysis of sets of trajectories of mechanical systems. Issue 1 (2016)

• Record Type: Journal Article
• Authors: Slyn'ko, V.I.
• Is Part Of: Journal of applied mathematics and mechanics. Volume 80:Issue 1(2016)
• Page Start: 24
• Page End: 32
• Publication Date: 2016
• Subjects: Mechanics, Analytic -- Periodicals; Mechanics, Applied -- Periodicals; Applied mathematics -- Periodicals; Mécanique analytique -- Périodiques; Mécanique appliquée -- Périodiques; 531.01515
• DOI: 10.1016/j.jappmathmech.2016.05.005
• Languages: English
• ISSNs: 0021-8928

Abstract

Abstract: The evolution of geometric measures (volume, surface area) of sets of attainability of linear controlled mechanical systems with constant parameters is studied. Lyapunov's direct method, the comparison method, and theory of mixed volumes are used. Based on the general comparison theorem, estimates are obtained for the solutions of differential equations with a generalized Hukuhara derivative that describe the evolution of regions of attainability. For linear controlled systems with one degree of freedom, the maximum boundedness conditions are obtained for the area of the set of attainability. Examples of the application of the obtained results are given.