Hostname: page-component-cb9f654ff-fg9bn Total loading time: 0 Render date: 2025-08-16T05:27:39.231Z Has data issue: false hasContentIssue false
  • English
  • Français

The Second Solution of Mathieu's Differential Equation

Published online by Cambridge University Press:  24 October 2008

S. Goldstein
S. Goldstein
Affiliation:
St John's College, Isaac Newton Student
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Mathieu functions of period π and 2π have recently been constructed by the help of analysis similar to that developed by Laplace, Kelvin, Darwin and Hough to find the free tides symmetrical about the axis of a rotating globe. The purpose of this note is to show that a similar construction can be carried out for the second solution of the Mathieu equation, when one solution is periodic in π or 2π, by the help of analysis similar to that used for forced tides. The construction is effected in a form suitable for numerical computation.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 24 , Issue 2 , April 1928 , pp. 223 - 230
Copyright
Copyright © Cambridge Philosophical Society 1928

References

* Trans. Camb. Phil. Soc., Vol. XXIII, p. 303 (1927).Google ScholarSee also Ince, , Proc. Roy. Soc. Edin., Vol. XLVI, p. 20 and p. 316 (1926), and Vol. XLVII, p. 294 (1927).Google Scholar

† Lamb, , Hydrodynamics, fifth edition, p. 313.Google Scholar

‡ Proc. Edin. Math. Soc., Vol. XXXIII, p. 2 (1915);Google ScholarProc. Camb. Phil. Soc., Vol. XXIII, p. 47 (1926).Google Scholar

§ Proc. Edin. Math. Soc., Vol. XXXIV, p. 4 (1916); Vol. XLI, p. 26 (1923); Vol. XLIV, p. 57 (1926).Google Scholar

* Trans. Camb. Phil. Soc., Vol. XXIII, p. 330.Google Scholar

* Trans. Camb. Phil. Soc., Vol. XXIII, p. 303.Google Scholar

* This point was overlooked in Trans. Camb. Phil. Soc., Vol. XXIII, p. 330, where F was taken as 1.Google Scholar