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

单词

Conformal Solution

释义

Conformal Solution

By letting , the Real and Imaginary Parts of mustsatisfy the Cauchy-Riemann Equations and Laplace's Equation, so they automatically provide a scalarstream function. If aphysical problem can be found for which the solution is valid, we obtain a solution--which may have been very difficultto obtain directly--by working backwards. Let

(1)

the Real and Imaginary Parts then give

			(2)
			(3)

For ,

			(4)
			(5)

which is a double system of Lemniscates (Lamb 1945, p. 69).For

			(6)
			(7)

This solution consists of two systems of Circles, and

is the Potential Function for twoParallel opposite charged line charges (Feynman et al. 1989, §7-5; Lamb 1945, p. 69). For

			(8)
			(9)

gives the field near the edge of a thin plate (Feynman et al. 1989, §7-5).For

			(10)
			(11)

This is two straight lines (Lamb 1945, p. 68).For

(12)

gives the field near the outside of a rectangular corner (Feynman et al. 1989, §7-5).For

(13)

			(14)
			(15)

These are two Perpendicular Hyperbolas, and

is the Potential Function near themiddle of two point charges or the field on the opening side of a charged Right Angleconductor

(Feynman 1989, §7-3).

See also Cauchy-Riemann Equations, Conformal Map, Laplace's Equation

References

Feynman, R. P.; Leighton, R. B.; and Sands, M. The Feynman Lectures on Physics, Vol. 1. Redwood City, CA: Addison-Wesley, 1989.

Lamb, H. Hydrodynamics, 6th ed. New York: Dover, 1945.

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