تقرير
Singularly perturbed dynamics of the tippedisk
| العنوان: | Singularly perturbed dynamics of the tippedisk |
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| المؤلفون: | Sailer, Simon, Leine, Remco I. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Mathematical Physics Physics (Other) |
| مصطلحات موضوعية: | Physics - Classical Physics, Mathematical Physics, Mathematics - Dynamical Systems, Physics - Applied Physics |
| الوصف: | The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disk, being reminiscent to (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global analysis of the reduced system is pursued using the framework of singular perturbation theory. It is shown how the presence of friction leads to slow-fast dynamics and the creation of a two-dimensional slow manifold. Furthermore, it is revealed that a bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation leads to an explanation of the inversion phenomenon. In particular, a closed-form condition for the critical spinning speed for the inversion phenomenon is derived. Hence, the tippedisk forms an excellent mathematical-mechanical problem for the analysis of global bifurcations in singularly perturbed dynamics. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1098/rspa.2021.0536 |
| URL الوصول: | http://arxiv.org/abs/2109.02542 |
| رقم الأكسشن: | edsarx.2109.02542 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1098/rspa.2021.0536 |
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