Geodesic
Algebraic integrability for minimum energy curves
Kybernetika, Tome 51 (2015) no. 2, pp. 321-334

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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.
DOI : 10.14736/kyb-2015-2-0321
Classification : 13N15, 34A34, 34C07, 34C14, 34H05
Keywords: Darboux polynomials; drag power; Euler–Lagrange equations; grading; integrability; vector fields 
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Yudin, Ivan; Silva Leite, Fátima. Algebraic integrability for minimum energy curves. Kybernetika, Tome 51 (2015) no. 2, pp. 321-334. doi: 10.14736/kyb-2015-2-0321

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