Correction of Stability Curves in Hill-Meissner's Equation

where x = d2x/dt2, w2 and a2 are real constants, and sgn z = 1 for z > 0, sgn z = -1 for z a > 0 in 1918 [1], and later by van der Pol and Strutt for the general case, in 1928 [3]. Since then, these transition curves [3] have been referred to in many papers, without correction (e.g. [4], [5]). The author has noticed that some correction is necessary for those transition curves, since there exists appreciable error in at least several points on the published curves. From these reasons, we present more accurate transition curves obtained by using a digital computer. It is easy to write solutions x(t) and x(t) from t = 0 to t = 7r, and from t = 7r to t = 277r respectively. Combining these solutions at t = ir so that x(t) and x(t) are continuous, we have solutions x(277r) and ?(277r) as a linear combination of the initial conditions x(O) and x(O). In short, x(O) and x(O) are transformed into x(2ir) and ?(27r) by a linear transformation. The characteristic equation of this transformation is given by the following equation [3]: