The Schuler Pendulum's Fatal Flaw

Abstract

Schuler himself genially but clearly warned here and there in his 1923 paper that he had not proved his principle, and indicated that the general proof was not within the range of his own limitations, thus inviting his readers to be critical of what amounted to interesting suggestions cheerfully offered. Professor Stratton's commentary (Journal, 21, 507), ‘The Schuler pendulum and inertial navigation’, by its scope, clearness and authenticity, could make effectual the remark that Schuler's calculation of acceleration is not correct except in one and the same great circle and possibly a few other special cases. Schuler jumps to the conclusion that it holds for any spherical motion, thus neglecting much of kinematics. The following standard analysis uses the moving trihedral and the intrinsic equations of ordinary differential geometry. There are many other methods having their own advantages.