A forced damped oscillation framework for undulatory swimming provides new insights into how propulsion arises in active and passive swimming

PLoS Comput Biol. 2013;9(6):e1003097. doi: 10.1371/journal.pcbi.1003097. Epub 2013 Jun 13.


A fundamental issue in locomotion is to understand how muscle forcing produces apparently complex deformation kinematics leading to movement of animals like undulatory swimmers. The question of whether complicated muscle forcing is required to create the observed deformation kinematics is central to the understanding of how animals control movement. In this work, a forced damped oscillation framework is applied to a chain-link model for undulatory swimming to understand how forcing leads to deformation and movement. A unified understanding of swimming, caused by muscle contractions ("active" swimming) or by forces imparted by the surrounding fluid ("passive" swimming), is obtained. We show that the forcing triggers the first few deformation modes of the body, which in turn cause the translational motion. We show that relatively simple forcing patterns can trigger seemingly complex deformation kinematics that lead to movement. For given muscle activation, the forcing frequency relative to the natural frequency of the damped oscillator is important for the emergent deformation characteristics of the body. The proposed approach also leads to a qualitative understanding of optimal deformation kinematics for fast swimming. These results, based on a chain-link model of swimming, are confirmed by fully resolved computational fluid dynamics (CFD) simulations. Prior results from the literature on the optimal value of stiffness for maximum speed are explained.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Animals
  • Models, Biological
  • Muscle Contraction
  • Swimming / physiology*

Grant support

This work was supported by National Science Foundation Grant CBET-0828749, CBET-1066575, and CMMI-0941674 (to NAP). BEG acknowledges research support from the National Science Foundation (NSF award OCI-1047734). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.