In this paper, we make an overview of the existing algorithms concerning the discrete curvature estimation. We extend the Worring and Smeulders [WS93] classification to new algorithms and we present a new and purely discrete algorithm based on discrete osculating circle estimation.

The geometrical structure of the magnetic field is a critical character in the magnetospheric dynamics. Using the magnetic field data measured by the Cluster constellation satellites, the geometrical structure including the curvature radius, directions of curvature and normal of the osculating planes of the magnetic field lines within the current sheet/neutral sheet have been investigated. The ...

1 Under the microscope 1.1 Osculating spaces of homogeneous varieties Let G be a simply connected complex semisimple Lie group, g its Lie algebra, and g its tensor algebra. The universal envelopping algebra of U(g) is the quotient of this tensor algebra by the ideal generated by the elements xy ? yx ? x; y], x; y 2 g. This quotient algebra inherits a ltration from the natural grading of the ten...

This work presents a precise analytical model to reconstruct the line-of-sight vector target satellite over time, as required by angles-only relative navigation systems for application rendezvous missions. The includes effects of geopotential, featuring: propagation in mean orbital elements (up second-order expansion), two-way osculating/mean elements’ conversion (second-order J2 and up given d...

For a hypothetical planet on a highly eccentric orbit, we have calculated the osculating orbital parameters and its closest approaches to Earth and Moon over a period of 750 kyr. The approaches which are close enough to influence the climate of the Earth form a pattern comparable to that of the past climatic changes, as recorded in deep sea sediments and polar ice cores.

We previously obtained a congruence modulo four for the number of real solutions to many Schubert problems on a square Grassmannian given by osculating flags. Here, we consider Schubert problems given by more general isotropic flags, and prove this congruence modulo four for the largest class of Schubert problems that could be expected to exhibit this congruence.