title: Simplified dynamic model for the motility of irregular echinoids.
abstract: Inspired by the locomotion mechanism of sea urchins, we study the locomotion of an irregular echinoid by means of a simplified dynamical model. We prove that if two conjectures are assumed, the geometrical arrangement of the five ambulacral petals of irregular echinoids should form a eutactic star in order to optimize motility. We firstly propose an adequate "measure" of eutacticity that allows us to to verify the statistical tendency to such a property for a representative collection of fossil specimens. Next, regarding dynamics, the biological advantage of eutactic stars is addressed as a minimal path problem. Finally, we study the stability of some eutactic stars under small perturbations.
authors.affiliation: Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Apartado Postal 1-1010, Querétaro 76000, México.
authors.forename: J L
authors.initials: JL
authors.lastname: Aragón
authors.forename: A
authors.initials: A
authors.lastname: Gómez-Rodríguez
authors.forename: M
authors.initials: M
authors.lastname: Torres
mesh_terms: D000818:Animals; D049628:Body Size / Q000502:physiology*; D003198:Computer Simulation; D005684:Gait / Q000502:physiology*; D008124:Locomotion / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical; D012617:Sea Urchins / Q000033:anatomy & histology* / Q000502:physiology*