Gyroscope mount treated as a dynamical system with Hamiltonian mechanics turns out to be chaotic


Gyroscope mount treated as a dynamical system with Hamiltonian mechanics turns out to be chaotic


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  1. This video shows a simulation of the gyroscope frame and gimbals based on the Hamiltonian formalism.

    The background shows the projected position of the object that has a trail.

    The system is expressed in terms of the rotations angles for the frame and the two inner gimbals thus having three degrees of freedom. The frame and the two gimbals are assumed to be the only masses in the system and are set to be 1.

    The system can effectively be reduced to two degrees of freedom due to one constant of motion. The simulation is performed using higher order symplectic integrators.

    It came as a surprise to me that chaos can occur for this dynamical system with three “apparently” uncoupled and individually non-chaotic rotations.

    Consequently, the well-acclaimed toy gyroscopes are chaotic by nature, even in the idealized non-friction form.

    Full video link, that includes also regular (non-chaotic) motion

    https://www.youtube.com/watch?v=c03gRtwDmK0

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