Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 41 - 1922  

Research Article

The Vibrations of a Particle about a Position of Equilibrium—Part III

The Significance of the Divergence of the Series Solution

Dr Bevan B. Baker

In the two parts of this investigation previously published it has been shown that the solution in terms of elliptic functions represents the motion of the particular dynamical system under consideration throughout the whole range of values of s and g for which a real solution exists, except for those values for which s = 2g and k = 1, but that, on the other hand, the series solution is convergent and represents the motion only so long as

S0013091500003667_eqn1

for values of s and g for which the sign of this inequality is reversed the trigonometric series representing the solution are divergent. It is of importance to investigate what discontinuities, if any, of the system correspond to values of s and g which lie on the boundary of the region of convergence; the present part is concerned primarily with showing that under such circumstances no discontinuity of the system exists, thus confirming the suggestions made in Part I., § 12.

(Accepted November 10 1922)

(Received August 27 1922)