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Flapping ight dynamics constitutes a multi-body, nonlinear, time-varying system. The two major simplifying assumptions in the analysis of apping ight stability are neglecting the wing inertial e ects and averaging the dynamics over the apping cycle. The challenges resulting from relaxing these assumptions naturally invoke the geometric control theory as an appropriate analysis tool. In this work, a reduced-order model (extracted from the full model derived in the rst part of this work) for the longitudinal apping ight dynamics near hover is considered and represented in a geometric control framework. Then, combining tools from geometric control theory and averaging, the full dynamic stability as well as balance analyses of hovering insects are performed.
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Periodic tilings and auxetic deployments
We investigate geometric characteristics of a specific planar periodic framework with three degrees of freedom. While several avatars of this structural design have been considered in materials science under the name of chiral or missing rib models, all previous studies have addressed only local properties and limited deployment scenarios. We describe the global configuration space of the framework and emphasize the geometric underpinnings of auxetic deformations. Analogous structures may be considered in arbitrary dimension.
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- Award ID(s):
- 1703765
- PAR ID:
- 10546994
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Mathematics and Mechanics of Solids
- Volume:
- 26
- Issue:
- 2
- ISSN:
- 1081-2865
- Format(s):
- Medium: X Size: p. 199-216
- Size(s):
- p. 199-216
- Sponsoring Org:
- National Science Foundation
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