2005/07/17 | 静电波[Electrostatic Wave]
类别(Ω〖物理〗) | 评论(0) | 阅读(46) | 发表于 09:30
A standing electrostatic wave has equation
(1)

To find the potential energy, note that
(2)

and


(3)

The kinetic energy is
(4)

Now, the equations defining the generalized coordinates x and p do not depend on time. Furthermore, the force is derivable from a conservative potential, so it follows that H is a constant of motion given by
(5)

Now non-dimensionalize this with a dimensionless parameter ,
(6)

Define
(7)

(8)

(9)

(10)

Then the equation becomes
(11)

Hamilton's equations then become
(12)


(13)

The fixed points occur when
(14)

(15)

so they are
(16)

However, there are also fixed points at
0

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