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Normal coordinates exist on a normal neighborhood of a point p in M. A normal neighborhood U is an open subset of M such that there is a proper neighborhood V of the origin in the tangent space T p M, and exp p acts as a diffeomorphism between U and V. On a normal neighborhood U of p in M, the chart is given by: :=: The isomorphism E, and ...
The GF method, sometimes referred to as FG method, is a classical mechanical method introduced by Edgar Bright Wilson to obtain certain internal coordinates for a vibrating semi-rigid molecule, the so-called normal coordinates Q k. Normal coordinates decouple the classical vibrational motions of the molecule and thus give an easy route to ...
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the line perpendicular to the tangent line to the curve at the point. A normal vector of length one is called a unit normal vector.
The lemma allows the exponential map to be understood as a radial isometry, and is of fundamental importance in the study of geodesic convexity and normal coordinates. Introduction [ edit ]
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
Choosing a local coordinate system determines a local section of this bundle, which can then be used to pull back the Christoffel symbols to functions on M, though of course these functions then depend on the choice of local coordinate system. For each point, there exist coordinate systems in which the Christoffel symbols vanish at the point. [16]
A normal vector to a strictly convex surface can be used to uniquely define a surface position. n-vector is an outward-pointing normal vector with unit length used as a position representation. [1] For most applications the surface is the reference ellipsoid of the Earth, and thus n-vector is used to represent a horizontal position.
A normal section at is determined by letting = ^ (the surface normal at ). Another normal section, known as the reciprocal normal section, results from using the surface normal at . Unless the two points are both on the same parallel or the same meridian, the reciprocal normal section will be a different path than the normal section.