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Limit trajectories in a non-holonomic system of a ball moving inside a spherical cavity
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SYSNO ASEP 0505748 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Limit trajectories in a non-holonomic system of a ball moving inside a spherical cavity Author(s) Náprstek, Jiří (UTAM-F) RID, ORCID, SAI
Fischer, Cyril (UTAM-F) RID, SAI, ORCIDNumber of authors 2 Source Title Journal of Vibration Engineering & Technologies. - : Springer - ISSN 2523-3920
Roč. 8, č. 2 (2020), s. 269-284Number of pages 16 s. Publication form Print - P Action The 14th International Conference on Vibration Engineering and Technology of Machinery. VETOMAC XIV. /14./ Event date 10.09.2018 - 13.09.2018 VEvent location Lisbon Country PT - Portugal Event type WRD Language eng - English Country DE - Germany Keywords non-holonomic systems ; dynamic stability ; nonlinear dynamics ; limit trajectories ; Appell-Gibbs approach Subject RIV JM - Building Engineering OECD category Civil engineering R&D Projects GC17-26353J GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support UTAM-F - RVO:68378297 UT WOS 000522457000002 EID SCOPUS 85071194292 DOI 10.1007/s42417-019-00132-1 Annotation The area of tuned mass dampers is a wide field of inspiration for theoretical studies in nonlinear dynamics and dynamic stability. In the paper, the authors analyze the regular and distinctive patterns of the free motion of a ball type tuned mass damper. The governing differential system modeling movement of a heavy ball rolling inside a spherical cavity is formulated and investigated, six degrees of freedom with three non-holonomic constraints and no slipping are assumed. Predominance of the Appell-Gibbs approach over the conventional Lagrangian procedure is pointed out when complicated non-holonomic systems are in question. General properties of the differential system in the normal form are discussed and possibilities of further investigation using semianalytical methods are outlined. Simultaneously, a wide program of numerical simulation is presented concerning the homogeneous system with a number of initial condition settings and other parameter variants. A number of limit trajectories are extracted and physically interpreted. The shape and general character of regular solutions within individual domains delimited by these limits are analyzed in order to facilitate a practical application of this theoretical background. Assumptions of further investigation are outlined. Workplace Institute of Theoretical and Applied Mechanics Contact Kulawiecová Kateřina, kulawiecova@itam.cas.cz, Tel.: 225 443 285 Year of Publishing 2020 Electronic address https://doi.org/10.1007/s42417-019-00132-1
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