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

Krzysztof Krakowski, Fátima Silva Leite (2014)

Kybernetika

We present an algorithm to generate a smooth curve interpolating a set of data on an n -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...

An example of a non-degenerate precession possessing two distinct pairs of axes

Giancarlo Cantarelli, Corrado Risito (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the present paper we provide an interesting example of a non-degenerate precession possessing two distinct pairs p , f , p ′ , f ′ of axes of precession and figure. Thus the problem arises of the existence of classes of precessions possessing a unique axis of precession and a unique axis of figure. In the fourth section we show that the class of non-degenerate regular precessions enjoys this property.

Geometry of the rolling ellipsoid

Krzysztof Andrzej Krakowski, Fátima Silva Leite (2016)

Kybernetika

We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two....

The dynamics of the drum mower blade

Bartoň, Stanislav (2019)

Programs and Algorithms of Numerical Mathematics

The drum mower blade is freely rotatable around the fastening pin. During the operation of the mower, the centrifugal force and the resistance of the mowing material act on it. The presented article studies the effect of these forces on the behavior of the blade, in particular its oscillation around the steady state, depending on the properties of the cut material.

The geometry of Newton's law and rigid systems

Marco Modugno, Raffaele Vitolo (2007)

Archivum Mathematicum

We start by formulating geometrically the Newton’s law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. For constrained systems we have intrinsic and extrinsic viewpoints, with respect to the environmental space. Multi–particle systems are modelled on n -th products of the pattern model. We apply the above scheme to discrete rigid systems. We study the splitting of the tangent and cotangent environmental space into the three components of center...

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