{'fraction_non_alphanumeric': 0.010935601458080195, 'fraction_numerical': 0.0, 'mean_word_length': 6.042735042735043, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Global Asymptotic Stabilization of a Spinning Top With Torque Actuators Using Stereographic Projection

The dynamical equations for a spinning top are derived in which theorientation is specified by a complex variable using stereographic projectionof Poisson's equations. Necessary and sufficient conditions for Lyapunovstability of the uncontrolled motion of the spinning top are derived usingthe Energy-Casimir method. Control laws that globally asymptoticallystabilize the spinning top to the sleeping motion using two torque actuatorsare synthesized by employing techniques from the theory of systems in cascadeform and generalized using Hamilton-Jacobi-Bellman theory with zero dynamics.In short, this paper provides a nice example where the interplay betweendynamics and control leads to elegant and powerful results.