Application of ultraspherical polynomials to non-linear oscillations. II. Free oscillations
Authors:
Harry H. Denman and Y. King Liu
Journal:
Quart. Appl. Math. 22 (1965), 273-292
MSC:
Primary 65.60
DOI:
https://doi.org/10.1090/qam/199965
MathSciNet review:
199965
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Additional Information
- Harry H. Denman and James E. Howard, Application of ultraspherical polynomials to non-linear oscillations. I. Free oscillation of the pendulum, Quart. Appl. Math. 21 (1963/64), 325–330. MR 155052, DOI https://doi.org/10.1090/S0033-569X-1964-0155052-3
Tables of the Chebyshev polynomials, National Bureau of Standards, Applied Mathematics Series 9 (U. S. Government Printing Office, 1952), Introduction
- N. W. McLachlan, Ordinary non-linear differential equations in engineering and physical sciences. 2nd ed, Oxford University Press, New York, 1956. MR 0093612
B. O. Pierce and R. M. Foster, A short table of integrals, 4th Edition, Ginn and Co., Boston, 1956, p. 99–102
- Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and physicists, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Bd LXVII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954. MR 0060642
E. Jahnke, F. Emde and F. Lösch, Tables of higher functions, 6th Edition, McGraw-Hill, New York, 1960
- Phillip Franklin, Methods of Advanced Calculus, McGraw-Hill Book Company, Inc., New York, 1944. MR 0010896
G. N. Watson, Theory of Bessel functions, 2nd Edition, Cambridge University Press, 1958, p. 369, eq. (8)
H. H. Denman, Computer generation of optimized subroutines, Jour. Assoc. Comp. Mach. 8 (1961) 1
- N. Kryloff and N. Bogoliuboff, Introduction to Non-Linear Mechanics, Annals of Mathematics Studies, No. 11, Princeton University Press, Princeton, N. J., 1943. MR 0007461
H. H. Denman and J. E. Howard, Application of ultraspherical polynomials to non-linear oscillations. I. Free oscillation of the pendulum, Q. Appl. Math. 21 (1964) 325
Tables of the Chebyshev polynomials, National Bureau of Standards, Applied Mathematics Series 9 (U. S. Government Printing Office, 1952), Introduction
N. W. McLachlan, Ordinary non-linear differential equations, 2nd Edition, Oxford University Press, London, 1956, p. 24–31, p. 39–40
B. O. Pierce and R. M. Foster, A short table of integrals, 4th Edition, Ginn and Co., Boston, 1956, p. 99–102
P. F. Byrd and M. D. Friedmann, Handbook of elliptic integrals for engineers and physicists, Springer, Berlin, 1954, p. 50
E. Jahnke, F. Emde and F. Lösch, Tables of higher functions, 6th Edition, McGraw-Hill, New York, 1960
P. Franklin, Methods of advanced calculus, McGraw-Hill, New York, 1944, p. 392
G. N. Watson, Theory of Bessel functions, 2nd Edition, Cambridge University Press, 1958, p. 369, eq. (8)
H. H. Denman, Computer generation of optimized subroutines, Jour. Assoc. Comp. Mach. 8 (1961) 1
N. Kryloff and N. Bogoliuboff, Introduction to non-linear mechanics, Princeton University Press, Princeton, 1943; N. Bogoliuboff and A. Mitropolsky, Asymptotic methods in the theory of non-linear oscillations, 2nd Edition, Gordon and Breach, New York, 1961
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Article copyright:
© Copyright 1965
American Mathematical Society