Estimation of the displacement of Purcell's swimmer

This code estimates the position of the centre of the central link of the Purcell's three-link swimmer by applying a square gait.

The objective of this code is to plot the displacement of the central link of Purcell's swimmer in a figure versus time. The parameters of the Purcell's swimmer, i.e., its length, radius, viscosity of the fluid, and gait amplitude must be defined. For more information, see:

• Nuevo-Gallardo C, Traver JE, Tejado I, Vinagre BM. Purcell’s Three-Link Swimmer: Assessment of Geometry and Gaits for Optimal Displacement and Efficiency. Mathematics. 2021; 9(10):1088. DOI: https://doi.org/10.3390/math9101088

There are four files, which must be saved in the same folder:

• Plot_Displacement.mlx: it is a script that plots the displacement of the centre of central link of the Purcell's swimmer versus time. It can be run in order to obtain a figure.
• PurcellDynamic.m: it is a function that estimates the displacement of the centre of the central link.
• SquareGait.m: it is a gait applied to the lateral links of the swimmer. It can be modified to another type of gait, such as circular.
• odeRK.m: it is a function that solves nonstiff differential equations through the Runge-Kutta method. It solves the differential equation of the velocity of the swimmer to obtain the displacement.