求曲线方程

倪举鹏

柔性绳子长度1，一端固定，一端拉水平，放手，在重力下，求时间t时候，绳子的曲线方程。

倪举鹏

最后是周期摆动还是混沌

TSC999

美国有个力学分析软件，能模拟绳子的运动情况。如果不是软绳而是一根细棍，那是容易人工计算的。

markfang2050

这个问题很复杂。涉及复杂的运动方程。有论文发表了的。

markfang2050

kolodner1955，mack1958，coomer2001，Guven_2013_New_J._Phys._15_113055

markfang2050

REFERENCES
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of strings.
3. N. J. ZABUSKY 1962 Journal of Mathematical Physics 3, 1028}1039. Exact solution for the
vibrations of a nonlinear continuous model string.
4. S. ANTMAN 1991 Non-linear Problems in Elasticity. Berlin: Springer, Applied Mathematical
Sciences 107.
5. D. A. LEVINSON 1977 American Journal of Physics 45, 680}681. Natural frequencies of a hanging
chain.
6. J. P. McCREESH, T. L. GOODFELLOW and A. H. SEVILLE 1975 American Journal of Physics 43,
646}648. Vibrations of a hanging chain of discrete links.
7. A. B.WESTERN 1980 American Journal of Physics 48, 54}56. Demonstration for observing J
0
(x) on
a resonant rotating vertical chain.
8. R. W. TUCKER and C. WANG 1999 Journal of Sound and <ibration 224, 123}165. An integrated
model for drill-string dynamics.
9. W. B. FRASER 1993 Philosophical &#185;ransactions of Royal Society of &#184;ondon A 342, 439}468. On the
theory of ring spinning.
10. F. ZHU, R. SHARMA and C. D. RAHN 1997 ASME Journal of Applied Mechanics 64, 676}683.
Vibrations of ballooning Elastic Strings.
11. I. KOLODNER 1955 Communications in Pure and AppliedMathematics 8, 395}408. Heavy rotating
string*a non-linear eigenvalue problem.
12. J. M. ORTEGA and W. G. POOL, JR 1981 An Introduction to Numerical Methods for Di+erential
Equations. London: Pitman.
13. H. B. KELLER 1970. Numerical Methods for &#185;wo-Point Boundary Problems. New York: Blaisdell.
14. D. MEADE 1998. A Maple implementation of the simple shooting method. Department of
Mathematics, ;niversity of South Carolina, Columbia, SC 29208, ;.S.A.
15. T. J. HEALEY, 1990 Quarternary Journal of Applied Mathematics 48, 679}698. Stability and
bifurcation of rotating non-linearly elastic loops.

倪举鹏

为什么我发的帖子问题都如此难