Kybernetika 51 no. 2, 321-334, 2015

Algebraic integrability for minimum energy curves

Ivan Yudin and Fátima Silva LeiteDOI: 10.14736/kyb-2015-2-0321

Abstract:

This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.

Keywords:

vector fields, Darboux polynomials, drag power, Euler-Lagrange equations, grading, integrability

Classification:

34H05, 34A34, 34C07, 34C14, 13N15

paper.pdf

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