DYNAMIC COUPLING OF TETHERS IN LARGE SPACE MECHANICS

摘要

The mechanics of large spaces (MLS) is put in service to anticipate the specific behavior of large-scale tethers, proposed to equip the yet hypothetical space elevators in both fixed ends, free ends and mixed ends configurations for future space flights. The envisaged tools for such space transportation systems should be based on anchored carbon nano-tubes ribbons extending over the altitude of synchronous satellites, namely up to 100,000-km for the Earth. These newly developed nano-materials manifest extremely high mechanical properties, with high values of the speed of phonons in the structure, feature that is closely related to the propagation of mechanical perturbations. Although in theory the speed of phonons goes very high, in fact the speed of sound is expected to lie somewhere around 25000-m/s. Due to extreme length, large time delays of up to 3 hours are expected to appear between the cause and its mechanical effect during elastic oscillations of tethered systems. Especially affected are the mixed eigen-oscillations where important dynamic coupling manifests. An extension of the mathematical principles of the mechanics of continua to the relative motion is proposed. Four different types of time derivatives define the new conditions. The Reynolds transport theorem of the derivative is proved not to depend on the reference system, as already considered by Onicescu. The theory is used in this application for the 1-D time-relaxed definition of the derivatives of physical quantities involved. This tool is offered for further development of mechanics with time relaxation.