Optimal time task in saccadic eye movement

This article is devoted to fast goal-directed human eye movements. Such movements are described in few ways. One of them is the time-optimal problem model. It this work, the saccade – fast single conformable ballistic eye movement, is under consideration. Saccadic eye trajectory is described by time-optimal task solution. Differential equations system are based on pendulum model. It defines control moment applied from extraocular muscles to eye globe and movement of it. Main feature of the system is all values in suggested system have physical meaning and were found in published experimental investigations. Consideration of the moment applied from extraocular muscles to eye glob as control is main difference of the system from other models for eye movement in submitted works. In this case, the open-loop system has two real roots and one zero. The particular case of the ratio of real roots of 1:3 is analyzed in the article. As a result of modelling, trajectory characteristics closed to the saccades observed in experimental studies is obtained. On the basis of the constructed model, the parameters of the synthesized saccades were compared with the parameters obtained on the experimental sample. The obtained models can be used both for problems of physiology and medicine, and for constructing virtual reality environments. For example, when developing 3D interfaces, the use of a mathematical model makes it possible to optimize the elements arrangement using game theory.