Multi-mode oscillations of a mechanical system with higher-order singularity

Abstract This article is based on earlier author’s works on the behavior of mechanical systems with a singular configuration space. We obtained exact analytical expressions for the constraints providing multi-mode oscillations of a double mathematical pendulum. It was found that there are infinitely...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 1959; no. 1; pp. 12026 - 12031
Main Author Kalnitsky, V S
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.07.2021
Subjects
Configurations
Mathematical analysis
Mechanical systems
Oscillation modes
Pendulums
Singularities
Smoothness
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Summary:Abstract This article is based on earlier author’s works on the behavior of mechanical systems with a singular configuration space. We obtained exact analytical expressions for the constraints providing multi-mode oscillations of a double mathematical pendulum. It was found that there are infinitely many modes of oscillations determined by the degree of degeneracy at a singular point in the configuration space of the pendulum. The problem of a double pendulum motion with an elliptical constraint, posed by the author earlier, received a complete solution, both theoretical and experimental. For such a constraint, there are exactly two different oscillation modes: symmetric and asymmetric. Each mode can be realized by selecting the system parameters and is completely determined by the smoothness of the trajectory in the configuration space with a singularity. In the study we used only standard tools of classical analytical mechanics.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1959/1/012026