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By A. W. Babister

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Sample text

Mathematics supplies various methods of investigation of differential equations. Derivation of equations of motion for the task of dynamics is an informal process of coupling of a physical model of the investigated object with methods of research of the mathematical model. In all problems of dynamics, simplicity and clearness of the form of equations of motion is important and, consequently, to a considerable degree, the success of research is determined by proper selection of the variables describing the motion.

The mechanical character of the discretisation of this model is obvious. As comparisons show, calculations with this model are well coordinated with calculations with the non-linear model with distributed parameters even in the case of a weakly tensed string [79]. Taking into account the bending and torsional stiffness of the cable, which could be important in the modelling of processes of deployment and retrieval of TSS, will influence the dynamics of the string and hence will create additional problems with ongoing discussions concerning the proper modelling.

8 Dependence of µ1 , µ1 /2, µ2 on increasing energy of longitudinal oscillations, c∗ = 100. 4). For a ω11 relatively stiff connection and certain parameters of motion if (r2 − d)/r0 1, it is possible to construct the approached solution for the motion with losing connection. 9 Appropriate variations of maximal, minimal and mean values of r. 36). Within the framework of the limited statement of the task, that is, the length of the tethered system is small compared to the radius of orbit, the regular properties of rotational TSS motion under the action of disturbances of different physical nature are studied.

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