An algorithm based on rolling to generate smooth interpolating curves on ellipsoids

Krakowski, Krzysztof; Leite, F. Silva

doi:10.14736/kyb-2014-4-0544

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…The no-twist conditions become u T p0 E n ⊂ T ⊥ p0 E n and u T ⊥ p0 E n ⊂ T p0 E n . By the same reasoning as in the spherical case, we reach the conclusion that u ∈ m, which is in agreement with results in [32]. 4.…”

Section: Examplessupporting

confidence: 90%

A unifying approach for rolling symmetric spaces

Krakowski¹,

Machado²,

Leite³

2021

JGM

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The main goal of this paper is to present a unifying theory to describe the pure rolling motions of Riemannian symmetric spaces, which are submanifolds of Euclidean or pseudo-Euclidean spaces. Rolling motions provide interesting examples of nonholonomic systems and symmetric spaces appear associated to important applications. We make a connection between the structure of the kinematic equations of rolling and the natural decomposition of the Lie algebra associated to the symmetric space. This emphasises the relevance of Lie theory in the geometry of rolling manifolds and explains why many particular examples scattered through the existing literature always show a common pattern.

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Section: Examplessupporting

confidence: 90%

A unifying approach for rolling symmetric spaces

Krakowski¹,

Machado²,

Leite³

2021

JGM

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show abstract

“…If one knows how to solve the kinematic equations of the rolling ellipsoid, at least for some simple curves, this approach provides an algorithm to solve the interpolation problem explicitly. Illustration of this algorithms has been done for the ellipsoid equipped with a non-Euclidean metric in [16] and for other Riemannian manifolds in [10]. The same idea has been proposed in [5] to solve multiclass classification problems in the context of pattern recognition.…”

Section: Introductionmentioning

confidence: 99%