A Unit Quaternion-based Spherical Trigonometry and a New Two-carrier Phase-quadrature Quaternion Modulation System

A new Hyperspherical trigonometry based on Quaternion ́s Algebra is introduced. Spatial curves on the surface of the unit-quaternion hypersphere are described in the parametric form. A draft of a new Continuous Quaternion Modulation System is presented, in which two modulation signals are used to drive paths in the normalized 4D-hypersphere. The outline of a PLL-based demodulation is also sketched.