|
|||||
|
|
Perturbation solutions of the Carson–Cambi equation |
|
| Authors: | Barbara Epstein Richard Barakat |
| Institution: | Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts USA |
| Abstract: | The periodic differential equation (1+ε cos t)y̋ + py = 0, hereby termed the Carson–Cambi equation, is the simplest second-order differential equation having a periodic coefficient associated with the second derivative. Provided |ε|<1, which is the case we examine, then the differential equation is a Hill's equation and thus possesses regions of stability and instability in the p–ε plane. Ordinary perturbation theory is employed to obtain the stable (periodic) solutions to ε3. Two-timing theory is employed to obtain solutions for values of k near the critical points k = ±, ±, ±. Three-timing is employed to extend the solution near k = ±. The solutions of the Carson–Cambi equation are compared with the solutions of the corresponding Mathieu equation. |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ | |