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Overdamping in gyroscopic systems composed of high-loss and lossless components
Multi angle
Authors : Figotin, Alexander (Author of the conference)
CIRM (Publisher )
37J05 - General theory, relations with symplectic geometry and topology
37J15 - Symmetries, invariants, invariant manifolds, momentum maps, reduction
37J40 - Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
70H03 - Lagrange's equations
70H05 - Hamilton's equations
70H09 - perturbation theories
CIRM (Publisher )
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Abstract :
Using a Lagrangian framework, we study overdamping phenomena in gyroscopic systems composed of two components, one of which is highly lossy and the other is lossless. The losses are accounted for by a Rayleigh dissipative function. We prove that selective overdamping is a generic phenomenon in Lagrangian systems with gyroscopic forces and give an analysis of the overdamping phenomena in such systems. Central to the analysis is the introduction of the notion of a dual Lagrangian system and this yields significant improvements on some results on modal dichotomy and overdamping.
MSC Codes : 37J05 - General theory, relations with symplectic geometry and topology
37J15 - Symmetries, invariants, invariant manifolds, momentum maps, reduction
37J40 - Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
70H03 - Lagrange's equations
70H05 - Hamilton's equations
70H09 - perturbation theories
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/05/16 Conference Date : 21/04/16 Subseries : Research talks arXiv category : Spectral Theory ; Mathematical Physics Mathematical Area(s) : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:48:54 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-04-21_Figotin.mp4 
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Information on the Event
Event Title : Spectral theory of novel materials / Théorie spectrales des nouveaux matériauxEvent Organizers : Exner, Pavel ; Kotani, Motoko ; Kuchment, Peter ; Zagrebnov, Valentin A. Dates : 18/04/2016 - 22/04/2016 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1399.html
Citation Data
DOI : 10.24350/CIRM.V.18962403Cite this video as: Figotin, Alexander (2016). Overdamping in gyroscopic systems composed of high-loss and lossless components. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18962403 URI : http://dx.doi.org/10.24350/CIRM.V.18962403 |
See Also
- [Multi angle] Twisted equivariant $\mathrm{K}$-theory and topological phases / Author of the conference Kubota, Yosuke.
- [Multi angle] Gysin maps and bulk-edge correspondence / Author of the conference Matsuo, Shinichiroh.
- [Multi angle] Topological nature of the Fu-Kane-Mele invariants / Author of the conference De Nittis, Giuseppe.
- [Post-edited] Emergent anyons in quantum Hall physics / Author of the conference Rougerie, Nicolas.
Bibliography
- Figotin, A., & Welters, A. (2016). On overdamping phenomena in gyroscopic systems composed of high-loss and lossless components. Journal of Mathematical Physics, 57(4), 042902 - http://dx.doi.org/10.1063/1.4944721
