Parametric acceleration – the effect of inward pull of the golf club at impact stage


Koryo Miura, 3–9-7 Tsurukawa, Machida, Tokyo 195–0061, Japan. E-mail:


The inward pull motion at the impact stage of the golf swing commonly observed with expert players was investigated in this paper. First, a model of nonconcentrated rotation was studied. It was found that, for a mass rotating around a pivot, if the pivot is moved in the direction opposite to the direction of centrifugal force of the mass, the kinetic energy of the mass could be increased. The increase is a result of the mutual action of the two governing factors of the system, which are the centripetal force and the pull velocity. A special type of equation of motion governs this phenomenon

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, and the parameter in the second term of the left-hand side of the equation ξ˙ characterizes its behaviour. The phenomenon is called the parametric acceleration, following the parametric excitation of vibration problems also governed by a similar equation. Second, the golf swing was investigated using the above finding. In the golf swing, the club is accelerated by the hands in a tangential direction. Theoretically, the additional acceleration of the clubhead could be achieved by pulling the club in the radial direction at impact stage, assuming that the centrifugal force of the clubhead is fully developed. To test this idea, an emulation using a modified double-link model was carried out. It was shown that the clubhead velocity could be increased substantially by the inward pull motion of the club at the impact stage, at which point no other means of acceleration is available. Discussions include the actual movement of the body for the inward pull, the efficiency of the pull motion and application to other sports.