“Point-Point Distance--3-D”的概念、定义、习题解题方法及翻译-数学辞典

单词

Point-Point Distance--3-D

释义

Point-Point Distance--3-D

The Line Element is

(1)

so the Arc Length between the points

and

(2)

and the quantity we are minimizing is

(3)

Finding the derivatives gives

			(4)
			(5)

and

			(6)
			(7)

so the Euler-Lagrange Differential Equations become

			(8)
			(9)

These give

(10)

(11)

Taking the ratio,

(12)

(13)

(14)

which gives

(15)

(16)

Therefore,

and

, so the solution is

(17)

which is the parametric representation of a straight line with parameter

. Verifying the Arc Length gives

(18)

where

(19)

(20)

See also Point-Point Distance--1-D, Point-Point Distance--2-D,Point-Quadratic Distance

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