Algebraic integrability for minimum energy curves

Yudin, Ivan; Leite, F. Silva

doi:10.14736/kyb-2015-2-0321

Cited by 2 publications

(2 citation statements)

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“…Based on some of the invariants given above, authors in [16] provided a very interesting study of the Euler-Lagrange equation for Euclidean spaces using the theory of Darboux polynomials. However, this study was inconclusive and our purpose here is to show the behavior of the solutions of the proposed optimization problem for certain Riemannian manifolds.…”

Section: Proposition 1 the Quantitymentioning

confidence: 99%

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Path Planning Trajectories in Fluid Environments

Machado

Leite

Monteiro

2018

2018 13th APCA International Conference on Control and Soft Computing (CONTROLO)

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This paper deals with the problem of finding a mission path that minimizes acceleration and drag while a vehicle moves from an initial position to a final target in fluid environments. A variational problem will be formulated in the general context of manifolds, where the energy functional depends on acceleration and drag forces. The corresponding Euler-Lagrange equations will be derived. Questions regarding the integrability of the Euler-Lagrange equations are the main challenge of this problem even when the geometry of the configuration space is not taken into consideration. This is mainly due to the fact that the power needed to overcome the drag forces is proportional to the cube of the speed. A numerical optimization approach will be presented in order to obtain approximate solutions for the problem in some particular configuration spaces.

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Section: Proposition 1 the Quantitymentioning

confidence: 99%

“…As we will see, the presence of the drag term increases substantially the complexity of the problem even when the problem is only formulated on a Euclidean space. Algebraic integrability properties of the Euler-Lagrange equations in Euclidean spaces have been partially studied in [16] using the theory of Darboux polynomials.…”

Section: Introductionmentioning

confidence: 99%