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A Compact Differential Formula for the First Derivative of a Unit Quaternion Curve
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1996
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Integral GeometryEngineeringGeometric Partial Differential EquationGeometryUnit Quaternion CurveEducationFirst DerivativeGlobal AnalysisKinematicsGeometric MechanicsComplex GeometryCompact Differential Formula
This paper presents a compact differential formula for the first derivative of a unit quaternion curve defined on SO(3) or S3. The formula provides a convenient way to compute the angular velocity of a rotating 3D solid. We demonstrate the effectiveness of this formula by deriving the differential properties of various unit quaternion curves1–5 at the curve end points.