Effect of rotation on sloshing in low-gravity

摘要

The theory of sloshing in low-gravity is extended to include rotation of the spacecraft. In low-gravity without rotation, surface tension is the only force that constrains the free surface. The Coreolis and centrifugal forces are added to the force balance when a spacecraft rotates. The equations of motion with the accompanying boundary conditions are solved in the linear approximation with the three relevant forces included. A geometry with circular symmetry is assumed. The analysis is analytic and the resulting formulas are evaluated by computation. The damping of the resonant modes is determined using boundary layer theory. The pressure field is integrated over the walls of the container to find the forces and torques due to sloshing. The results are expressed as transfer functions in the frequency domain from the motion of the container to the forces and torques on the spacecraft. These transfer functions are also stated in the Laplace transform s-domain. Then, they can be combined with the models of the controls and dynamics to form an overall transfer function for the motion of the spacecraft. A new type of resonance is found that results from the frequency dependence of the waveform. The method is applied to the NASA mission Gravity Probe-B and some results are presented.