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The Vibrations of a Particle about a Position of Equilibrium—Part 2 :The Relation between the Elliptic Function and Series Solutions

Published online by Cambridge University Press:  20 January 2009

Bevan B. Baker
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In a previous paper, entitled the “Vibrations of a Particle about a Position of Equilibrium,” by the author in collaboration with Professor E. B. Ross (Proc. Edin. Math. Soc., XXXIX, 1921, pp. 34–57), a particular dynamical system having two degrees of freedom was chosen and solutions of the corresponding differential equations were obtained in terms of periodic series and also in terms of elliptic functions. It was shown that for certain values of the frequencies of the principal vibrations, the periodic series become divergent, whereas the elliptic function solution continues to give finite results.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , February 1921 , pp. 34 - 49
Copyright
Copyright © Edinburgh Mathematical Society 1921

References

* In the previous paper by Baker and Ross, loc. cit., this equation, given on page 40, contains a misprint in the last term.