In this paper, we develop a beam tracking scheme for an orthogonal frequency division multiplexing (OFDM) Integrated Sensing and Communication (ISAC) system with a hybrid digital analog (HDA) architecture operating in the millimeter wave (mmWave) band. Our tracking method consists of an estimation step inspired by radar signal processing techniques, and a prediction step based on simple kinematic equations. The hybrid architecture exploits the predicted state information to focus only on the directions of interest, trading off beamforming gain, hardware complexity and multistream processing capabilities. Our extensive simulations in arbitrary trajectories show that the proposed method can outperform state of the art beam tracking methods in terms of prediction accuracy and consequently achievable communication rate, and is fully capable of dealing with highly non-linear dynamic motion patterns.