Comments on “a regular perturbation technique for non-linearly coupled oscillators in resonance”

✍ Scribed by B.K. Shivamoggi

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 54 KB
• Volume: 101
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(85)80045-6

✦ Synopsis

Mickens gave a regular perturbation technique for obtaining uniformly valid solutions to systems of weakly coupled non-linear oscillators which satisfy a resonance condition. However, this technique is inadequate in describing the dynamics of a system of weakly coupled non-linear oscillators in a resonance condition. It does not at all describe the essential exchange of energy taking place continually between the two oscillators under a resonance condition, as shown by the numerical calculations of Ford and Waters [2] for a similar system. Indeed, if the dissipation in the system represented by the parameters /xt and/~2 is eliminated, Mickens' technique gives only the null solution!