On the “bead, hoop and spring” (BHS) dynamical system

Here, we make the theoretical and numerical analysis of the non-linear equation describing the evolution of the “bead, hoop and spring” (BHS) dynamical system derived by Ochoa and Clavijo in (Eur. J. Phys. 27:1277–1288, 2006 ). In particular, we solve by standard techniques of non-linear physics an...

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Bibliographic Details
Published inNonlinear dynamics Vol. 56; no. 3; pp. 315 - 323
Main Author Rousseaux, G.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.05.2009
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Linear equations
Mechanical Engineering
Nonlinear analysis
Nonlinear equations
Numerical analysis
Original Paper
Phase transitions
Singularities
Vibration
Non-linear oscillations
Singularity
Duffing-like system
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Summary:Here, we make the theoretical and numerical analysis of the non-linear equation describing the evolution of the “bead, hoop and spring” (BHS) dynamical system derived by Ochoa and Clavijo in (Eur. J. Phys. 27:1277–1288, 2006 ). In particular, we solve by standard techniques of non-linear physics an approximation of their equation neglecting the centrifugal effect before giving a more mathematical and exact treatment. The analogy with phase transitions is underlined. We point out the existence of finite-time singularities in the phase-space and we derive a criterion for possible oscillations.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-008-9407-6