Abstract
Time differences between gold and silver medallist at Olympic alpine ski races are less than 0.01 second. One factor leading to this difference is the lines taken between the numerous gates passed through while speeding down a ski slope. As the primary attempt to solve the problem the quickest descent line between two points on a ski slope is determined by applying a direct optimal control theory. The theory converts the optimal control problem into the parameter optimization problem and uses a nonlinear programming method. The present problem is described in terms of an objective function, state variables and control variables. The objective function is the time between two points which should be passed by skiers. The control variables are the edging angles at the N+1 nodes which are obtained by dividing the final time by N. The quickest lines between two gates under different conditions are presented.
