Melnikov-Arnold Integral
المؤلف:
Chirikov, B. V.
المصدر:
"A Universal Instability of Many-Dimensional Oscillator Systems." Phys. Rep. 52
الجزء والصفحة:
264-379
11-9-2021
1331
Melnikov-Arnold Integral
![A_m(lambda)=int_(-infty)^inftycos[1/2mphi(t)-lambdat]dt,](https://mathworld.wolfram.com/images/equations/Melnikov-ArnoldIntegral/NumberedEquation1.gif) |
(1)
|
where the function
 |
(2)
|
describes the motion along the pendulum separatrix. Chirikov (1979) has shown that this integral has the approximate value
![A_m(lambda) approx <span style=]() {(4pi(2lambda)^(m-1))/(Gamma(m))e^(-pilambda/2) for lambda>0; -(4e^(-pi|lambda|/2))/((2|l|)^(m+1))Gamma(m+1)sin(pim) for lambda<0. " src="https://mathworld.wolfram.com/images/equations/Melnikov-ArnoldIntegral/NumberedEquation3.gif" style="height:94px; width:296px" /> |
(3)
|
REFERENCES:
Chirikov, B. V. "A Universal Instability of Many-Dimensional Oscillator Systems." Phys. Rep. 52, 264-379, 1979.
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