“Harmonic Addition Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Harmonic Addition Theorem

释义

Harmonic Addition Theorem

To convert an equation of the form

(1)

to the form

(2)

expand (2) using the trigonometric addition formulas to obtain

(3)

Now equate the Coefficients of (1) and (3)

			(4)
			(5)

(6)

(7)

and we have

			(8)
			(9)

Given two general sinusoidal functions with frequency

			(10)
			(11)

their sum

can be expressed as a sinusoidal function with frequency


			(12)

Now, define

(13)

(14)

Then (12) becomes

(15)

Square and add (13) and (14)

(16)

Also, divide (14) by (13)

(17)

(18)

where

and

are defined by (16) and (17).

This procedure can be generalized to a sum of harmonic waves, giving

(19)

where

			(20)
			(21)

and

(22)

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