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Floquet stability analysis of the longitudinal dynamics of two hovering model insects
- Source :
- Journal of The Royal Society Interface. 9:2033-2046
- Publication Year :
- 2012
- Publisher :
- The Royal Society, 2012.
-
Abstract
- Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered—a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier–Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed.
- Subjects :
- Physics
Floquet theory
Computer simulation
Biomedical Engineering
Biophysics
Longitudinal static stability
Equations of motion
Bioengineering
Aerodynamics
Mechanics
Moths
Models, Biological
Biochemistry
Insect flight
Biomaterials
Control theory
Flight, Animal
Stability theory
Animals
Flapping
Research Articles
Biotechnology
Subjects
Details
- ISSN :
- 17425662 and 17425689
- Volume :
- 9
- Database :
- OpenAIRE
- Journal :
- Journal of The Royal Society Interface
- Accession number :
- edsair.doi.dedup.....232afe5502caca24fbd29a252f1f7ce8