Dynamics of A Large Streerable Radio Telescope Antenna

An analytical model having a moderate number of degrees of freedom was formulated in order to represent approximately the dynamic behavior of a large steerable radio telescope antenna structure. Techniques for synthesizing simplified mathematical models for complex structures are described. A model consisting of nine rigid bodies with a total of 33 degrees of freedom was devised to represent a 210-ft diameter antenna structure having approximately 4,800 degrees of freedom. Determination of the mass, inertia, and stiffness properties of the model is presented. A method of establishing equations of motion is presented and demonstrated with a simple example having only six degrees of freedom. A tabular method for generating the coefficients in the equations is described in detail. This orderly approach to writing the equations is useful for either a hand or a computer solution. Several types of computer programs were utilized in the analysis in combination with a certain amount of hand calculation.