ISSN:
1432-1467
Keywords:
nonlinear oscillations
;
shooting methods
;
homoclinic chaos
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary We study the equations for two-dimensional irrotational motion induced in a rectangular tank of water which is forced to oscillate horizontally in a periodic fashion (“shallow water sloshing”). The problem reduces to a second-order non-autonomous ordinary differential equation. We rigorously show the existence of many solutions obtained previously by numerical computations, and in addition we show that there are many other bounded solutions. We use simple shooting to obtain irregular solutions of the kind obtained by the methods of dynamical systems. In addition, we obtain a kind of “kneading” theory whereby we can order the initial conditions according to the pattern of “spikes” exhibited by the solutions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01209067
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