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An elastic rod model for anguilliform swimming.
1Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA. mcmillen@princeton.edu
Journal of Mathematical Biology
|September 15, 2006
Summary
This study models eel-like swimming using an elastic rod theory, revealing passive elasticity affects body shape and reduces speed compared to prior models. Tapered bodies with specific activation patterns enhance swimming performance.
Area of Science:
- Biomechanics
- Fluid Dynamics
- Robotics
Background:
- Anguilliform (eel-like) swimming is a complex locomotion strategy.
- Previous models often simplify the physics of eel swimming, such as Taylor's assumption of prescribed shape.
Purpose of the Study:
- To develop a geometrically exact model for anguilliform swimming.
- To investigate the role of passive elasticity and activation patterns on swimming dynamics.
- To compare a new elastic rod model with existing rigid-link models.
Main Methods:
- Developed a geometrically exact theory for an elastic rod actuated by intrinsic curvature.
- Employed discretization for numerical simulations of the nonlinear partial differential equations.
- Compared simulation results with previous chain models.
Main Results:
- Passive elasticity causes deviations from Taylor's prescribed shape, leading to time-periodic motion and reduced speeds.
- Muscle activations driven by motoneuronal spike trains and calcium dynamics produce near-sinusoidal body shapes.
- Laterally uniform activation ensures stable straight swimming; differential activation enables stable turns.
Conclusions:
- The elastic rod model provides a more realistic representation of anguilliform swimming than simplified models.
- Body geometry (tapering) and activation patterns significantly influence swimming speed and maneuverability.
- Optimized caudal activation in tapered bodies can lead to faster swimming speeds.
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