A CLOSED-FORM SOLUTION TO THE PLANAR DYNAMICS OF A FLEXIBLE SPACE STATION MODEL

The governing equations of motion for a flexible space station model f ree to undergo both in-plane librational and vibrational motions are d eveloped. The non-linear and coupled equations are not amenable to any closed-form solution. A simplified set of non-linear equations, captu ring the essential features of the system, is obtained. An approximate analytical technique which is an extension of Butenin's Method is dev eloped. This technique can be employed for a system with an arbitrary number of degrees-of-freedom and is used to obtain a closed-form solut ion for the flexible space station model. Its validity is assessed thr ough comparison with the numerical solution of the original governing equations. Good agreement between the results suggests that a consider able amount of useful information can be obtained without resorting to time consuming and expensive numerical simulation.