Nonlinear systems - modeling, estimation, and stability

0494186 - ÚTAM 2019 RIV GB eng M - Monography Chapter
Náprstek, Jiří - Fischer, Cyril
Appell-Gibbs approach in dynamics of non-holonomic systems.
Nonlinear systems - modeling, estimation, and stability. London: IntechOpen, 2018 - (Reyhanoglu, M.), s. 3-30. ISBN 978-1-78923-404-6
R&D Projects: GA ČR(CZ) GC17-26353J
Institutional support: RVO:68378297
Keywords : Appell-Gibbs function * Lagrangian approach * non-holonomic systems * engineering applications
OECD category: Construction engineering, Municipal and structural engineering
https://www.intechopen.com/books/nonlinear-systems-modeling-estimation-and-stability

Hamiltonian functional and relevant Lagrange’s equations are popular tools in the investigation of dynamic systems. Various generalizations enable to extend the class of problems concerned slightly beyond conventional limits of Hamiltonian system. This strategy is very effective, particularly concerning two-dimensional (2D) and simpler threedimensional (3D) systems. However, the governing differential systems of most nonholonomic 3D systems suffer from inadequate complexity, when deduced using this way. Any analytical investigation of such a governing system is rather impossible and its physical interpretation can be multivalent. For easier analysis, particularly of systems with non-holonomic constraints, the Appell-Gibbs approach seems to be more effective providing more transparent governing systems. In general, the Appell-Gibbs approach follows from the Gaussian fifth form of the basic principle of dynamics. In this chapter, both Lagrangian and Appell-Gibbs procedures are shortly characterized and later their effectiveness compared on a particular dynamic system of a ball moving inside a spherical cavity under external excitation. Strengths and shortcomings of both procedures are evaluated with respect to applications.
Permanent Link: http://hdl.handle.net/11104/0287433