Search results for "Osculating circle"

Improved Method for Orbital Elements Differential Correction.

1990

As was pointed out by IAU in 1976, an important problem in fundamental astronomy is the improvement of the vernal equinox and equator positions. To this aim, it is necessary to know the accurate values of minor planets orbital elements. The classical methods of orbital elements differential corrections are based on linking the observations at different epochs considering equal derivatives respect to the initial and osculating elements. In this paper we present an improved method in which the least squares matrix coefficients is calculated from the integration of the Lagrange planetary equations and its derivatives.

Application of spaces of subspheres to conformal invariants of curves and canal surfaces

2013

A continuous circle of pseudo-arcs filling up the annulus

1999

We prove an early announcement by Knaster on a decomposition of the plane. Then we establish an announcement by Anderson saying that the plane annulus admits a continlous decomposition into pseudo-arcs such that the quotient space is a simple closed curve. This provides a new plane curve, "a selectible circle of pseudo-aics", and answers some questions of Lewis.

Spectral analysis of the Neumann-Poincaré operator and characterization of the stress concentration in anti-plane elasticity

2012

When holes or hard elastic inclusions are closely located, stress which is the gradient of the solution to the anti-plane elasticity equation can be arbitrarily large as the distance between two inclusions tends to zero. It is important to precisely characterize the blow-up of the gradient of such an equation. In this paper we show that the blow-up of the gradient can be characterized by a singular function defined by the single layer potential of an eigenfunction corresponding to the eigenvalue 1/2 of a Neumann–Poincare type operator defined on the boundaries of the inclusions. By comparing the singular function with the one corresponding to two disks osculating to the inclusions, we quant…

The constant osculating rank of the Wilking manifold

2008

We prove that the osculating rank of the Wilking manifold V3 = (SO (3) × SU (3)) / U• (2), endowed with the metric over(g, )1, equals 2. The knowledge of the osculating rank allows us to solve the differential equation of the Jacobi vector fields. These results can be applied to determine the area and the volume of geodesic spheres and balls. To cite this article: E. Macias-Virgos et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2007 Academie des sciences.

The horospherical geometry of surfaces in hyperbolic 4-space

2006

We study some geometrical properties associated to the contacts of surfaces with hyperhorospheres inH + 4 (−1). We introduce the concepts of osculating hyperhorospheres, horobinormals, horoasymptotic directions and horospherical points and provide conditions ensuring their existence. We show that totally semiumbilical surfaces have orthogonal horoasymptotic directions.

PLANE CURVE DIAGRAMS AND GEOMETRICAL APPLICATIONS

2007

Die Schmieghyperebenen an die Veronese-Mannigfaltigkeit bei Beliebiger Charakteristik

1982

By means of linear algebra a base-free definition of a Veronese variety V(n,r) is given and also an illuminating description of its osculating primes from which can be deduced in a general form and without difficulty the phenomena of degeneracy in case of small characteristics. (Instance best known: For characteristic 2 all tangents of a conic are confluent.) The last section investigates special problems for the V(1,r) in characteristic p: So the osculating primes of a V(1,p) intersect its node in a V(1,p-2). Furthermore it becomes clearer why for 2<r<¦K¦−1 no elation can fix a V(1,r) (in case of a perfect field).