One-Parameter Lorentzian Dual Spherical Movements and Invariants of the Axodes
Yanlin Li, Nadia Alluhaibi, Rashad A. Abdel-Baky
Abstract
E. Study map is one of the most basic and powerful mathematical tools to study lines in line geometry, it has symmetry property. In this paper, based on the E. Study map, clear expressions were developed for the differential properties of one-parameter Lorentzian dual spherical movements that are coordinate systems independent. This eliminates the requirement of demanding coordinates transformations necessary in the determination of the canonical systems. With the proposed technique, new proofs for Euler–Savary, and Disteli’s formulae were derived.
Topics & Concepts
Property (philosophy)Euler's formulaDual (grammatical number)Symmetry (geometry)Differential (mechanical device)Mathematical proofLine (geometry)Spherical coordinate systemEuler anglesComputer scienceMathematical analysisMathematicsPure mathematicsGeometryPhysicsEpistemologyArtPhilosophyLiteratureThermodynamicsMathematics and ApplicationsAlgebraic and Geometric Analysis3D Shape Modeling and Analysis