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Asymptotics of Damped Periodic Motions with Random Initial Speed

โœ Scribed by Yuliy Baryshnikov; Wolfgang Stadje

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
737 KB
Volume
189
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

We consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the probability law of the stopping position of the motion converges to a distribution depending only on the motion equation. Here the time of stopping is either a constant or the first time instant at which the velocity vanishes, and the initial velocity is of the form aU + p, where U is a fixed random variable and a and/or p tend to infinity.

๐Ÿ“œ SIMILAR VOLUMES

ASYMPTOTIC SOLUTION OF A CLASS OF NON-LI
ASYMPTOTIC SOLUTION OF A CLASS OF NON-LINEAR NON-AUTONOMOUS SYSTEMS WITH LARGE DAMPING UNDER MULTIPLE EXTERNAL PERIODIC FORCES
โœ Z. Zhang; R. Wang; S. Kusumoto ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 529 KB

Based on the KBM method, a new asymptotic method of calculation is presented, and applied to an extremely general non-linear, non-autonomous system with finite large damping under multiple external periodic forces: i.e., Asymptotic solutions for resonance and off-resonance vibrations are obtained.