2 articles for “Quaternions”

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Research ArticleOpen accessIn the keywordsVehicle-Fixed-Frame Adaptive Controller and Intrinsic Nonlinear PID Controller for Attitude Stabilization of a Complex-Shaped Underwater VehicleChanaka Thushitha Bandara, Lakmali Nadeesha Kumari, Sanjeeva Maithripala, Asanga RatnaweeraIn this study we present attitude stabilization using a vehicle-fixed-frame adaptive controller and an intrinsic nonlinear PID controller for a low-speed Autonomous Underwater Vehicle (AUV), of complex shape. Controlling an AUV poses a huge challenge because of the non-linearity, time variance and unpredictable external disturbance, as well as because its dynamics and hydrodynamic parameters are difficult to identify due to … …Journal of Mechatronics and Robotics, Vol. 4, Issue 1 · 7 Dec 2020 · 6,987 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsSplit-Quaternionic Representation of the Moving Frame for Timelike Surfaces in 3-Dimensional Minkowski SpacetimePaul BrackenThe moving frame and associated Gauss-Codazzi equations for surfaces in Minkowski three space are introduced. A split-quaternionic representation is used to identify the Gauss-Weingarten equations with a Lax pair representation. This Lax pair representaion is calculated and given explicitly. …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,725 accessesView PDF Cite