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

单词

Biharmonic Equation

释义

Biharmonic Equation

The differential equation obtained by applying the Biharmonic Operator and setting to zero.

(1)

In Cartesian Coordinates, the biharmonic equation is

In Polar Coordinates (Kaplan 1984, p. 148)


			(3)

For a radial function

, the biharmonic equation becomes


			(4)

Writing the inhomogeneous equation as

(5)

we have

(6)

(7)

(8)

(9)

(10)

Now use

(11)

to obtain

(12)

(13)


			(14)

The homogeneous biharmonic equation can be separated and solved in 2-D Bipolar Coordinates.

References

Kaplan, W. Advanced Calculus, 4th ed. Reading, MA: Addison-Wesley, 1991.

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