{"title":"An asymmetrical body: Example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect","authors":"","doi":"10.1016/j.cnsns.2024.108257","DOIUrl":null,"url":null,"abstract":"<div><p>We solved the Poisson equations, obtaining their exact solution in elementary functions for the rotation matrix of a free asymmetrical body with angular velocity vector lying on separatrices. This allows us to discuss the temporal evolution of Dzhanibekov’s nut directly in the laboratory system, where it is observed. The rotation matrix depends on two parameters with clear physical interpretation as a frequency and a damping factor of the solution. Qualitative analysis of the solution shows that it properly describes a single-jump Dzhanibekov effect.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424004428","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We solved the Poisson equations, obtaining their exact solution in elementary functions for the rotation matrix of a free asymmetrical body with angular velocity vector lying on separatrices. This allows us to discuss the temporal evolution of Dzhanibekov’s nut directly in the laboratory system, where it is observed. The rotation matrix depends on two parameters with clear physical interpretation as a frequency and a damping factor of the solution. Qualitative analysis of the solution shows that it properly describes a single-jump Dzhanibekov effect.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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