Loading...
Please wait, while we are loading the content...
Similar Documents
On an equation connected with the theory of triode oscillations
| Content Provider | Scilit |
|---|---|
| Author | Smith, R. A. |
| Copyright Year | 1952 |
| Description | This discussion is concerned with the periodic solutions of the differential equation where the parameter k is small. The equation arises from an investigation of the forced oscillations of a simple electrical circuit (6) containing a triode. The function f(x) is derived from the current-voltage characteristic of the triode and it has a roughly ⊂-shaped graph, with a flat bottom and some slight asymmetry. For a regenerative circuit, we have f(0) < 0. Van der Pol (5) considered the equation with f (x) = $x^{2}$ − 1, and he and later writers (1, 2, 4) have built up an extensive theory of triode oscillations for this ideal case. In practice, the graph of f(x) has a much flatter bottom than that of the function $x^{2}$ − 1, and it was asked by Cartwright ((3), p. 214) whether this flattening would alter the qualitative behaviour of the circuit near resonance. The main part of this paper is an attempt to answer this question. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/88A7273F1410C8AEF36F7E60149DFB43/S0305004100076465a.pdf/div-class-title-on-an-equation-connected-with-the-theory-of-triode-oscillations-div.pdf |
| Ending Page | 717 |
| Page Count | 20 |
| Starting Page | 698 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100076465 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 4 |
| Volume Number | 48 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1952-10-24 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
