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Singular solution
About: Singular solution is a research topic. Over the lifetime, 8842 publications have been published within this topic receiving 155069 citations.
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Book•
01 Apr 1989
TL;DR: This paper presents a meta-analyses of linear singular systems through system analysis via transfer matrix and feedback control of dynamic compensation for singular systems.
Abstract: Solutions of linear singular systems- Time domain analysis- Feedback control- State observation- Dynamic compensation for singular systems- Structurally stable compensation in singular systems- System analysis via transfer matrix- to discrete-time singular systems- Optimal control- Some further topics
3,020 citations
Book•
01 Jan 1968
TL;DR: The Singular Points of Complex Hypersurfaces (AM-61) as mentioned in this paper is a seminal work in the area of complex hypersurfaces, and is based on as mentioned in this paper.
Abstract: The description for this book, Singular Points of Complex Hypersurfaces. (AM-61), will be forthcoming.
2,676 citations
2,163 citations
TL;DR: In this paper, the authors compare the results of a singular solution of Navier's equations of motion of viscous fluid with the results obtained from many experiments, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved.
Abstract: 1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.
1,409 citations