This provides a natural realisation of the osculating circle to a curve, and the curvature spheres of a surface.
12.
If there is only one intersection point, which has multiplicity 4, the two conic sections are said to be osculating.
13.
The curve " C " may be obtained as the envelope of the one-parameter family of its osculating circles.
14.
Each constraint can be a point, angle, or curvature ( which is the reciprocal of the radius of an osculating circle ).
15.
There exists a circle in the osculating plane tangent to whose Taylor series to second order at the point of contact agrees with that of.
16.
If " P " is a vertex then " C " and its osculating circle have contact of order at least four.
17.
For most bodies, the osculating elements are relatively close to the proper elements because precession and perturbation effects are relatively small ( see diagram ).
18.
Given any curve and a point on it, there is a unique circle or line which most closely approximates the curve near, the osculating circle at.
19.
The first generalized curvature is called "'curvature "'and measures the deviance of from being a straight line relative to the osculating plane.
20.
The radial component is directed from the point " P " to the point where the perpendicular from an arbitrary fixed origin meets the osculating plane.
