The limitations on vibration isolation for microgravity space experiments are explored. These limitations result from the restricted interior space available for vibration isolation and the strokes required to achieve isolation. A one-degree-of-freedom representation of the experiment spacecraft system is used, and an ideal vibration actuator is assumed. The wall motion is characterized as sinusoidal at a single frequency. A kinematic representation results, and the problem becomes one of finding the minimum acceleration trajectory within a pair of moving walls. This optimal control problem can be solved via the calculus of variations; however, transcendental equations result. To obtain an analytic solution, the inequality constraints are dropped and initial and final conditions on the trajectory are added. The resulting control is optimal if the inequality constraints are still satisfied. Analysis yields a simple condition under which a closed-form solution is available. A suboptimal solution that always satisfies the inequality constraints is also presented. This solution is shown to have performance very close to optimal. The minimum experiment rms acceleration given the spacecraft vibration frequency and amplitude is obtained from the optimal and suboptimal solutions. Plots are presented, and the limitations on vibration isolation are discussed. These results demonstrate that isolation from low-frequency vibration requires more interior space than is available for vibration isolation on manned space orbiters.
