| Project/Area Number |
03044084
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| Research Category |
Grant-in-Aid for international Scientific Research
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| Allocation Type | Single-year Grants |
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| Section | Joint Research |
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| Research Institution | Kyoto University |
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Principal Investigator |
UEDA Yoshisuke Faculty of Eng., Kyoto University (Professor), 工学部, 教授 (00025959)
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| Co-Investigator(Kenkyū-buntansha) |
TOMPSON J.M. ロンドン大学, 教授
STEWART Hugh B Brookhaven National Laboratory. Applied Science Division. (Mathematician), 数学者
THOMPSON John M T Dept. of Civil Eng., University College London (Professor)
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| Project Period (FY) |
1991
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| Project Status |
Completed (Fiscal Year 1991)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1991: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | Dynamical systems / Power generation / Fractal basin boundary / Straddle orbit method / Chaotic transients / Bifurcations with indeterminate outcome / Capsize of ships / Ship stabilization mechanism |
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| Research Abstract |
The study of ordinary differential equations representing the dynamics of two coupled swings has been pursued using digital simulations and algorithms based on the geometrical theory of dynamical systems. These equations were derived from a simple model of dynamical stability of a simple electric power generation system involving two generators connected by a transmission line. Although this system has no chaotic attractors, there is a fractal basin boundary which is of fundamental relevance in determining the engineering stability properties. Substantial progress has been made in understanding the underlying structure of this fractal basin boundary by applying the straddle orbit method. However, there remain some important unanswered questions about this fractal structure which we hope to investigate the coming year.
Recently a new fundamental phenomenon in nonlinear dynamics has been discovered by the investigators : catastrophic bifurcations causing loss of stability followed by chao
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tic transients leading to one of several possible new attractor outcomes. In this project the ideas were pursued further to discover additional types of bifurcations with indeterminate outcome, according to the form of the initiating bifurcation. In addition to the already-known indeterminate saddle-node and chaotic blue sky catastrophe, new types include indeterminate transcritical and subcritical bifurcations have been discovered. These appear in simple prototypical nonlinear oscillators modelling forced oscillations in a potential well. Engineering applications include the capsize of ships in heavy seas. It appears that these phenomena are common and widespread in engineering problems.
Another nonlinear oscillator describing a proposed ship stabilization mechanism was studied, again using digital simulation and dynamical systems approaches. This oscillator includes a time delay term ; it was found that the destabilization of the system by gradually increasing the feedback gain results in the development of almost periodic oscillations and then chaotic behavior which is an immediate precursor of capsize. Less
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