Limit trajectories in a non-holonomic system of a ball moving inside a spherical cavity

0505748 - ÚTAM 2020 RIV DE eng J - Journal Article
Náprstek, Jiří - Fischer, Cyril
Limit trajectories in a non-holonomic system of a ball moving inside a spherical cavity.
Journal of Vibration Engineering & Technologies. Roč. 8, č. 2 (2020), s. 269-284. ISSN 2523-3920. E-ISSN 2523-3939.
[The 14th International Conference on Vibration Engineering and Technology of Machinery. VETOMAC XIV. /14./. Lisbon, 10.09.2018-13.09.2018]
R&D Projects: GA ČR(CZ) GC17-26353J
Institutional support: RVO:68378297
Keywords : non-holonomic systems * dynamic stability * nonlinear dynamics * limit trajectories * Appell-Gibbs approach
OECD category: Civil engineering
Impact factor: 1.889, year: 2020
Method of publishing: Limited access
https://doi.org/10.1007/s42417-019-00132-1

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.
Permanent Link: http://hdl.handle.net/11104/0297146