Abstract
Summary This paper introduces some ideas and general theorems pertaining to non-linear or mechanical systems. Thus in the case of a resistive network, the dissipation is divided into two parts—the "content" and "co-content"—which are duals of each other. The dissipation itself has stationary properties in linear but not (in general) in non-linear networks, but it can be shown that the "content" and "co-content" have stationary and additive properties in the non-linear case. The idea of "content" is extended to reactive systems, and it is shown that the total content of any system in motion is an invariant. This paper is intended as a companion to the paper by E. C. Cherry.
Keywords
Dual polyhedronContent (measure theory)DissipationInvariant (physics)MathematicsResistive touchscreenMotion (physics)Linear systemMathematical analysisPure mathematicsComputer sciencePhysicsThermodynamicsArtificial intelligenceMathematical physics
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Publication Info
- Year
- 1951
- Type
- article
- Volume
- 42
- Issue
- 333
- Pages
- 1150-1160
- Citations
- 123
- Access
- Closed
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Cite This
William Millar
(1951).
CXVI. Some general theorems for non-linear systems possessing resistance.
The London Edinburgh and Dublin Philosophical Magazine and Journal of Science
, 42
(333)
, 1150-1160.
https://doi.org/10.1080/14786445108561361
Identifiers
- DOI
- 10.1080/14786445108561361