Publicación: (SO(3) X T-4)-REDUCTION AND RELATIVE EQUILIBRIA FOR A RADIAL AXISYMMETRIC INTERMEDIARY MODEL FOR ROTO-ORBITAL MOTION
Fecha
2020
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JOURNAL OF GEOMETRY AND PHYSICS
Resumen
A GEOMETRICAL APPROACH TO A RADIAL INTERMEDIARY MODEL FOR AN AXISYMMETRIC RIGID BODY IN ROTO-ORBITAL MOTION IS PRESENTED. THE PRESENCE OF SYMMETRIES ENABLES A WELL-SUITED FORMULATION BY CHOOSING ACTION?ANGLE TYPE VARIABLES. SINGULARITIES ASSOCIATED WITH THE ANGLES ARE AVOIDED BY INTRODUCING EXTRA FICTITIOUS VARIABLES AND PERFORMING A SYMPLECTIC TRANSFORMATION LEADING TO A GLOBAL, QUATERNIONIC DOUBLE-CHART. THEN, MAKING USE OF THE AND SYMMETRY OF OUR MODEL, A FULL REDUCTION PROCESS BY STAGES IS CARRIED OUT, WHICH IN COMBINATION WITH THE CONSTRAINED DYNAMICS RELATED TO THE FICTITIOUS VARIABLES, LEADS TO A 1-DOF REDUCED-CONSTRAINED SYSTEM. OUR PROGRAM INCLUDES A PARAMETRIC ANALYSIS OF RELATIVE EQUILIBRIA AND A COMPLETE DESCRIPTION OF THE FIBERS IN THE RECONSTRUCTION OF THE REDUCED SYSTEM.
