Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Fátima Silva Leite"'
Publikováno v:
Mathematics, Vol 11, Iss 21, p 4540 (2023)
We discuss the rolling, without slipping and without twisting, of Stiefel manifolds equipped with α-metrics, from an intrinsic and an extrinsic point of view. We, however, start with a more general perspective, namely, by investigating the intrinsic
Externí odkaz:
https://doaj.org/article/f7ff26d8fc2642f38367018a16c850f6
Autor:
Knut Hüper, Fátima Silva Leite
Publikováno v:
Mathematics, Vol 11, Iss 16, p 3545 (2023)
Simple closed formulas for endpoint geodesics on Graßmann manifolds are presented. In addition to realizing the shortest distance between two points, geodesics are also essential tools to generate more sophisticated curves that solve higher order in
Externí odkaz:
https://doaj.org/article/966850833e5c4ebb98771d2d97f34984
This paper uncovers a large class of left-invariant sub-Rie\-mannian systems on Lie groups that admit explicit solutions with certain properties, and provides geometric origins for a class of important curves on Stiefel manifolds, called quasi-geodes
Externí odkaz:
http://arxiv.org/abs/1809.07013
Autor:
Luís Machado, Fátima Silva Leite
Publikováno v:
CONTROLO 2022 ISBN: 9783031100468
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::79fa61fe74978fa9cb1c4d82c0904fad
https://doi.org/10.1007/978-3-031-10047-5_35
https://doi.org/10.1007/978-3-031-10047-5_35
Publikováno v:
Lecture Notes in Electrical Engineering ISBN: 9783030586522
We study local existence and uniqueness for Riemannian cubics satisfying boundary conditions. We define the biexponential map and use it to relate initial and boundary data. We also describe biconjugate points along cubics by means of the biexponenti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::98c5930b98579374fafb79a7e3be1953
https://doi.org/10.1007/978-3-030-58653-9_31
https://doi.org/10.1007/978-3-030-58653-9_31
Publikováno v:
Lecture Notes in Electrical Engineering ISBN: 9783030586522
In this paper, we present a simplified geometric algorithm to generate interpolating splines on Grassmann and Stiefel manifolds, where position and velocity are required to change smoothly. In this construction, each spline segment is computed using
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51536b38fc3454e4e36f1c8e19105efc
https://doi.org/10.1007/978-3-030-58653-9_17
https://doi.org/10.1007/978-3-030-58653-9_17
Publikováno v:
Lecture Notes in Electrical Engineering ISBN: 9783030586522
In this paper we use a variational approach, combining holonomic and nonholonomic constraints, to find an equation for sub-Riemannian geodesics on the orthogonal group. This approach is extrinsic in nature and makes the paper fully self-contained and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1b99b3f39c11be86d6533f67afafc0ac
https://doi.org/10.1007/978-3-030-58653-9_26
https://doi.org/10.1007/978-3-030-58653-9_26
Autor:
Fatima Pina, Fátima Silva Leite
Publikováno v:
Lecture Notes in Electrical Engineering ISBN: 9783030586522
We present a detailed implementation of the De Casteljau algorithm to generate cubic splines that solve certain interpolation problems in the Grassmann manifold.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f215b2b3c4dcefac37164eff1edd8654
https://doi.org/10.1007/978-3-030-58653-9_23
https://doi.org/10.1007/978-3-030-58653-9_23
Publikováno v:
Handbook of Variational Methods for Nonlinear Geometric Data ISBN: 9783030313500
In this chapter we study solutions to certain interpolation problems on Riemannian manifolds. Our methodology is based on rolling motions of those manifolds considered as rigid bodies, subject to holonomic as well as non-holonomic constraints. Althou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b4b4fbb0c5fd0aaf287aef0eb3294542
https://doi.org/10.1007/978-3-030-31351-7_21
https://doi.org/10.1007/978-3-030-31351-7_21
Autor:
André Marques, Fátima Silva Leite
Publikováno v:
Journal of Geometric Mechanics. 14:105
This paper is devoted to rolling motions of one manifold over another of equal dimension, subject to the nonholonomic constraints of no-slip and no-twist, assuming that these motions occur inside a pseudo-Euclidean space. We first introduce a definit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ae9edc9279a7769e543da5102d60adae
https://doi.org/10.3934/jgm.2021033
https://doi.org/10.3934/jgm.2021033