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

Standard

Multi-mode oscillations of a mechanical system with higher-order singularity. / Kalnitsky, V. S.

In: Journal of Physics: Conference Series, Vol. 1959, No. 1, 012026, 01.07.2021.

Research output: Contribution to journal › Conference article › peer-review

BibTeX

@article{f50d56239c6c47248b0e6b59dd19a62b,

title = "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 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.",

author = "Kalnitsky, {V. S.}",

note = "Publisher Copyright: {\textcopyright} 2021 Published under licence by IOP Publishing Ltd.; International Scientific Conference on Mechanics {"}The Ninth Polyakhov's Reading{"}, ISCM 2021 ; Conference date: 09-03-2021 Through 12-03-2021",

year = "2021",

month = jul,

day = "1",

doi = "10.1088/1742-6596/1959/1/012026",

language = "English",

volume = "1959",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - Multi-mode oscillations of a mechanical system with higher-order singularity

AU - Kalnitsky, V. S.

PY - 2021/7/1

Y1 - 2021/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85111958160&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1959/1/012026

DO - 10.1088/1742-6596/1959/1/012026

M3 - Conference article

AN - SCOPUS:85111958160

VL - 1959

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012026

T2 - International Scientific Conference on Mechanics "The Ninth Polyakhov's Reading", ISCM 2021

Y2 - 9 March 2021 through 12 March 2021

ER -

ID: 86198766