Abstract: The largest radio telescope FAST is an important tool for human to explore the universe, with the characteristics of lightweight and convenient the cable-net structure reflector for the FAST is a new driving mechanism, but the flexible cable can experience tension and stiffness is very small, the positioning accuracy is low, which makes the dynamic modeling and analysis is very difficult. The mathematical model of the reflector for the FAST is set up by the variational principle, which brings a large number of nonlinear equation, a layer-wise substitution method to solve the non-linear equations of the mathematical model is proposed. The node location of the cable-net and tension of the main cable can be got by solving nonlinear equations of the mathematical model. The accurate position of all the nodes from the initial state to the tension state are achieved with the method, at the same time, the initial value of the nonlinear equations for the cable-net from the tension state to the working state has been provided. To show the validity of the method, the result of the initial state of a reduced model of the cable-net support structure of active reflector for the FAST is exhibited. from the calculation results obtained by the method we know that the solution accuracy is much higher than the design requirements.

Key words: Latitude main cable, Five-hundred-meter aperture spherical telescope(FAST), Layer-wise substitution method, Longitude main cable