Nonlinear transverse oscillations of the space elevator’s tether

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.