Vibrations of a pendulum consisting of a bob suspended from a wire: the method of integral equations
Author:
Hyun J. Ahn
Journal:
Quart. Appl. Math. 39 (1981), 109-117
MSC:
Primary 70J05; Secondary 45J05
DOI:
https://doi.org/10.1090/qam/613954
MathSciNet review:
613954
Full-text PDF Free Access
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Abstract: The vibrations of a vertical pendulum consisting of a bob suspended from a wire are studied by the method of integral equations and the composite method, respectively. The composite method combines the minimum principles and the method of integral equations. This problem consists of the fourth-order differential equation and the boundary conditions dependent on the eigenvalue parameter. Lower bounds are established for the lowest natural frequencies by both methods. Numerical results are presented. Both theoretical and computational efficiencies are illustrated and the method of integral equations is stressed.
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E. L. Ince, Ordinary differential equations, Dover, New York, 1956
H. Jeffreys and B. Jeffreys, Methods of mathematical physics, Cambridge University Press, New York, 1972
A. V. Laginestra and W. E. Boyce, Convergence and evaluation of sums of reciprocal powers of eigenvalues of boundary value problems nonlinear in the eigenvalue parameter, SIAM J. Math. Anal. 5, 64–90 (1974)
R. V. Southwell, Aero. Res. Comm. (U.K.), Reports and memoranda 486; H. Lamb and R. V. Southwell, The vibrations of a spinning disc, Proc. Roy. Soc. (A), 99, 272–280 (1921)
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K. Yosida, Lectures on differential and integral equations, Interscience, New York, 1960
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Article copyright:
© Copyright 1981
American Mathematical Society
