The position and velocity being given in all three co-ordinates, a certain osculating plane is determined for each instant in which the planet is moving at that instant.
The essential principle of Lagrange's elegant method consists in determining the variations of this osculating ellipse, the co-ordinates and velocities of the planet being ignored in the determination.
The flexural couples reduce to a single couple in the osculatingplane proportional to the curvature when the two flexural rigidities are equal, and in this case only.
The whole of the foregoing reasonings are applicable, not merely when A and B are actual regular cones, but also when they are the osculating regular cones of a pair of irregular conical surfaces, having a common apex at O.
It follows that the osculating plane of the curve formed by the string must contain the normal to the surface, i.
That is to say, the osculating plane at any point of a geodetic line contains the normal to the surface at that point.
It cuts the osculating plane in a line called the principal normal.
When a point of such a curve is given, the osculating plane is determined, hence all the curves through a given point with the same tangent have the same torsion.
An osculating plane of the curve (see S 38 below) is a tangent plane of the torse all along a generating line.
The osculatingplane at any point of such a curve is the nul-plane of the point with respect to the complex, and points of superosculation always coincide in pairs at the points of contact of stationary tangents.
It cuts the osculating plane in a circle, called the circle of absolute curvature; and the centre and radius of this circle are the centre and radius of absolute curvature.
The normal perpendicular to the osculating plane is called the binormal.
Developable surface; an envelop of the osculating planes of a curve.
The osculating plane of a curve at a given point may be constructed by considering it as the edge of regression of a developable surface; this construction presents some uncertainty in practice.
Determination of the osculating hyperboloid along a generatrix.
The osculating plane of the directrix at the point of contact touches the surface along this edge.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "osculating" in a variety of sentences. We hope that you will now be able to make sentences using this word.
