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Dynamics & control of an axisymmetric spinning top

Dynamics & control of an axisymmetric spinning top

Date13th Jan 2022

Time11:00 AM

Venue Google Meet: meet.google.com/ote-rrfk-hga

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Details

The dynamics of a spinning top is a classical problem in the mechanics literature. It manifests rich and complex dynamic behaviour. In this work, we investigate the dynamics and control of an axisymmetric spinning top with one point fixed. The governing equations of motion for such system are well-known in the literature and are in the form of a system of three coupled nonlinear differential equations. The literature has classified three distinct class of trajectories for this dynamical system. In this work, we track trajectories corresponding to each of these three classes. The trajectory tracking is performed in presence of impulsive disturbances on the precession and nutation variables. A linear feedback is used in order the track the desired trajectory. The control effort is in the form base acceleration to the ground frame along two mutually perpendicular horizontal directions. In the first part of the work, trajectories with steady precession are analyzed. The linearized equations of motion leads to a linear time-invariant (LTI) system. A control strategy implemented on the basis of linearized equations of motion is shown to track the reference trajectory for a number of test cases. In the second part of the work, nutation dynamics is incorporated. The linearized equations of motion in this case leads to a system of ordinary differential equations with periodic coefficients. Exploiting the theory of linear time-varying periodic (LTVP) system, a control strategy is implemented. Numerical simulations are shown to validate the efficacy of the proposed method.

Speakers

Anirudh Chandramouli

Mechanical Engineering