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.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Recurrent Holonomy—Anomalous Gyro Couplings and Possible Drives


    Contributors:

    Conference:

    SPACE, PROPULSION & ENERGY SCIENCES INTERNATIONAL FORUM: SPESIF‐2009 ; 2009 ; Huntsville (Alabama)


    Published in:

    AIP Conference Proceedings ; 1103 , 1 ; 294-301


    Publication date :

    2009-03-16


    Size :

    8 pages





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



    Recurrent Holonomy - Anomalous Gyro Couplings and Possible Drives

    Binder, B. | British Library Conference Proceedings | 2009


    Couplings for vehicle drives

    Maier, A. | Engineering Index Backfile | 1958



    Hydraulic couplings for marine main drives

    Großbritannien, Intelligence Objectives Sub-Committee | TIBKAT | 1945