research

The phenomenon of gimbal lock rose in prominence during the time  of NASA's Apollo program. Inside the inertial measurement unit of the Apollo spacecraft was a stable (inertial) platform about which the spacecraft rotated. The hinged platform was suspended in two gimbals to give it three degrees of freedom. Its role was to give an accurate measure of the spacecraft's orientation. At a particular orientation of the spacecraft, the gimbals became coplanar and control torques became ineffective at stabilizing the platform.

We present a numerical method which exploits the biorthogonal interpolating wavelet family, and second-generation wavelets, to solve initial–boundary value problems on finite domains. Our predictor-corrector algorithm constructs a dynamically adaptive computational grid with significant data compression, and provides explicit error control. Error estimates are provided for the wavelet representation of functions, their derivatives, and the nonlinear product of functions.