Geodesic
Nonlinear transverse oscillations of the space elevator’s tether
Matematičeskoe modelirovanie, Tome 23 (2011) no. 12, pp. 3-19

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The dynamics of free oscillations of superlong ($\sim$100 000 km) tether, anchored to the Earth's equator and extending above the geostationary orbit is investigated. Nonlinear transverse oscillations of the tether are considered in the rotating geographical axes, taking into account Earth’s gravitational centrifugal field. Continuous mathematical model of flexible inextensible tether with changing along the tether cross-sectional area is used. Numerical algorithms allowing study of the system motions for time intervals of dozens of main mode oscillations are developed. Various forms of restricted in the vicinity of vertical equilibrium motions are found, some scenarios of catastrophic instability development are defined. One of such scenarios is investigated analytically by constructing self-similar solution of some model problem.
Keywords: space elevator, space tether systems, space elevator dynamics, mathematical modeling of inextensible thread dynamics, self-similar solutions of partial differential equations. 
@article{MM_2011_23_12_a0,
     author = {Yu. A. Sadov and A. B. Nuralieva},
     title = {Nonlinear transverse oscillations of the space elevator{\textquoteright}s tether},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--19},
     publisher = {mathdoc},
     volume = {23},
     number = {12},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_12_a0/}
}
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Yu. A. Sadov; A. B. Nuralieva. Nonlinear transverse oscillations of the space elevator’s tether. Matematičeskoe modelirovanie, Tome 23 (2011) no. 12, pp. 3-19. http://geodesic.mathdoc.fr/item/MM_2011_23_12_a0/