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Title: Solving the discrete Euler–Arnold equations for the generalized rigid body motion
Authors: Cardoso, João R. 
Miraldo, Pedro
Keywords: Discrete Euler-Arnold equations; Matrix equation; Moser-Veselov equation; Optimization with orthogonal constraint; Orthogonal matrices; Skew-symmetric matrices
Issue Date: 2022
Publisher: Elsevier
Project: CMUC-UIDB/00324/2020 
Serial title, monograph or event: Journal of Computational and Applied Mathematics
Volume: 402
Abstract: We propose three iterative methods for solving the Moser-Veselov equation, which arises in the discretization of the Euler-Arnold differential equations governing the motion of a generalized rigid body. We start by formulating the problem as an optimization problem with orthogonal constraints and proving that the objective function is convex. Then, using techniques from optimization on Riemannian manifolds, the three feasible algorithms are designed. The first one splits the orthogonal constraints using the Bregman method, whereas the other two methods are of the steepest-descent type. The second method uses the Cayley-transform to preserve the constraints and a Barzilai-Borwein step size, while the third one involves geodesics, with the step size computed by Armijo’s rule. Finally, a set of numerical experiments are carried out to compare the performance of the proposed algorithms, suggesting that the first algorithm has the best performance in terms of accuracy and number of iterations. An essential advantage of these iterative methods is that they work even when the conditions for applicability of the direct methods available in the literature are not satisfied.
ISSN: 03770427
DOI: 10.1016/
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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