As a fundamental challenge, gluing different metric spaces to get the desired geodesic flow is a kind of metric engineering, which could be interesting for technical applications. Here it is shown that there is a strange attractor connecting spherical and hyperbolic space recurrently on the common tangential path of parallel transport and that this pure geometric attractor can promote a local hyperbolic (vortex) geodesic flow on a rotating spherically curved surface. The rapidity space metrics of spherical (gyroscopic) and hyperbolic (Thomas) rotated rotations (precession), which belong to the SO(3) Lorentz group, are connected by first geometric principles with some relations from spherical trigonometry establishing the geodesic attractor. The strange attractor arises from a recurrent holonomy based on magic precession and nutation angles as coupling singularities supporting equilibrium or limit cycle bifurcation vortex patterns on all scales. The resulting hyperbolic space‐time precession flux tube points outwards connecting to a distant spherically curved rotating surface, which could be extended to a network of spin/precession/nutation dynamics and patterns. The identification and stimulation can be assigned to special winding numbers characterizing the holonomy difference between the spherical precessions and the hyperbolic tube geometry. A possible utilization could be the generation of an artificial geodesic flow stimulated by an external precession dynamics controlled by the holonomy attractor, which could be relevant to space drives and gravitational wave generation.
Recurrent Holonomy—Anomalous Gyro Couplings and Possible Drives
SPACE, PROPULSION & ENERGY SCIENCES INTERNATIONAL FORUM: SPESIF‐2009 ; 2009 ; Huntsville (Alabama)
AIP Conference Proceedings ; 1103 , 1 ; 294-301
2009-03-16
8 pages
Conference paper
Electronic Resource
English
Recurrent Holonomy - Anomalous Gyro Couplings and Possible Drives
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