“Direction Cosine”的概念、定义、习题解题方法及翻译-数学辞典

单词

Direction Cosine

释义

Direction Cosine

Let be the Angle between and , the Angle between and , and the Angle between and . Then the direction cosines are equivalent to the coordinatesof a Unit Vector ,

(1)

(2)

(3)

From these definitions, it follows that

(4)

To find the Jacobian when performing integrals over direction cosines, use

			(5)
			(6)
			(7)

The Jacobian is

(8)

Using

			(9)
			(10)



			(11)


			(12)

Direction cosines can also be defined between two sets of Cartesian Coordinates,

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

Projections of the unprimed coordinates onto the primed coordinates yield


			(22)

			(23)

			(24)

and

			(25)
			(26)
			(27)

Projections of the primed coordinates onto the unprimed coordinates yield


			(28)

			(29)

			(30)

and

(31)

(32)

(33)

Using the orthogonality of the coordinate system, it must be true that

(34)

(35)

giving the identities

(36)

for

and

, and

(37)

for

. These two identities may be combined into the single identity

(38)

where

is the Kronecker Delta.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。