Dynamic behavior of the inextensible string
Author:
R. W. Dickey
Journal:
Quart. Appl. Math. 62 (2004), 135-161
MSC:
Primary 74K05; Secondary 74H99
DOI:
https://doi.org/10.1090/qam/2032576
MathSciNet review:
MR2032576
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Abstract: The two dimensional dynamic behavior of a geometrically exact inextensible string is discussed. A variety of exact solutions are described and various asymptotic theories are derived. The similarity between the motion of the inextensible string and galactic motion is described.
R. Courant and D. Hilbert, Methods of Mathematical Physics, VI. Interscience Publishers, New York, 1962
- Ignace I. Kolodner, Heavy rotating string—a nonlinear eigenvalue problem, Comm. Pure Appl. Math. 8 (1955), 395–408. MR 71605, DOI https://doi.org/10.1002/cpa.3160080307
- Stuart S. Antman, Nonlinear problems of elasticity, Applied Mathematical Sciences, vol. 107, Springer-Verlag, New York, 1995. MR 1323857
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
- J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
R. Courant and D. Hilbert, Methods of Mathematical Physics, VI. Interscience Publishers, New York, 1962
I. I. Kolodner, Heavy rotating string—a nonlinear eigenvalue problem, Comm. on Pure and App. Math. 8, 395–408 (1955)
S. S. Antman, Nonlinear Problems of Elasticity, Springer-Verlag, New York, 1995
E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill Book Co., New York, 1955
J. Stoker, Nonlinear Vibrations, Interscience Publishers, New York, 1950
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Article copyright:
© Copyright 2004
American Mathematical Society
