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Leonardo Solanilla

William O Clavijo

Yessica P Velasco

Abstract

The Cartesian-Newtonian paradigm of mechanics establishes that, within an inertial frame, a body either remains at rest or moves uniformly on a line, unless a force acts externally upon it. This crucial assertion breaks down when the classical concepts of space, time and measurement reveal to be inadequate. If, for example, the space is non-flat, an effective translation might occur from rest in the absence of external applied force. In this paper we examine mathematically the motion of a small object or lizard on an arbitrary curved surface. Particularly, we allow the lizard’s shape to undergo a cyclic deformation due exclusively to internal forces, so that the total linear momentum is conserved. In addition to the fact that the deformation produces a swimming event, we prove –under fairly simplifying assumptions that such a translationis some what directly proportional to the Gauss curvature of the surface at the point where the lizardlies.

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Keywords

Non-Euclidean Differential Geometry, Local Riemannian Geometry, Lagrangian Formalism, Equations of Motion.

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How to Cite
Solanilla, L., Clavijo, W., & Velasco, Y. (2018). Swimming in Curved Surfaces and Gauss Curvature. Universitas Scientiarum, 23(2), 319-331. https://doi.org/10.11144/Javeriana.SC23-2.sics
Section
Matemáticas y Estadística / Mathematics and Statistics / Matemática e Estatística
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