“Tangent Vector”的概念、定义、习题解题方法及翻译-数学辞典

单词

Tangent Vector

释义

Tangent Vector

For a curve with Position Vector , the unit tangent vector is defined by

			(1)
			(2)
			(3)

where

is a parameterization variable and

is the Arc Length. For a function given parametrically by

, the tangent vector relative to the point

is therefore given by

			(4)
			(5)

To actually place the vector tangent to the curve, it must be displaced by

.It is also true that

			(6)
			(7)
			(8)

where

is the Normal Vector,

is the Curvature, and

is the Torsion.

See also Curvature, Normal Vector, Tangent, Tangent Bundle, Tangent Plane, Tangent Space,Torsion (Differential Geometry)

References

Gray, A. ``Tangent and Normal Lines to Plane Curves.'' §5.5 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 85-90, 1993.

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