The Usage of Mathematical Models in Figure Skating

Figure skating is one of the most popular and beautiful winter sports included in the program of the Olympic Games. Figure skating is popular because it differs in high emotionality and expressiveness of movements.

I chose skating as a figure because I thought a lot of maths were involved, so there would be endless possibilities of what I could talk about this subject. It is one of the public sports, so often people start to learn figure skating since the preschool age. Since the ice-skating industry improved a lot in Russia, I became interested in this sport. I learned how to ice-skate in my childhood, however, I was always wondering how people do different elements? I started to wonder if there is the math behind the complex jumps and spins the figure skater does? I figured that types of maths involved in skating figures are angles, direction, speed, timing, inertia, and much more. Even though I am not a professional ice-skater I wanted to study the matters behind figure skating.

Arc movement is the main element of figure skating, and figure skating training begins with it. This element allows the skater to develop the speed necessary to perform other, more complex elements and is also a connecting link between these elements. When moving in an arc, the skater stands on one leg, and the blade of the ridge in contact with the ice with one rib. The skater does not move vertically, but at a certain angle to the horizon, because of which the trajectory of his movement is curved, and not straight. The curvature of the trajectory can be characterized by a physical parameter - the radius of curvature. When constructing the model of movement along an arc, the following assumptions were made:

• The skater is seen as a moving material point.
• The angle of the ridge to the vertical changes linearly.

Rotation around the vertical axis is an element of figure skating, in which the skater, standing on a supporting leg, rotates around an imaginary axis. The free leg can be pulled to the side or lifted. In the process of rotation, the skater can change rotation poses, coordinating their actions with the help of the free leg and arms. The approach to rotation is usually a movement about an arc half a circle long. The whole rotation process can be divided into two stages: grouping (the period for which the skater changes his moment of inertia, clutching his hands to the body) and rotation (the time for which the skater rotates around his axis, having a constant moment of inertia).

In modern figure skating, a large number of various elements are combined, the implementation of which requires good preparation. The initial period of training in this sport is not an easy process. The current trend in the development of figure skating is characterized by a pronounced tendency towards harmony in the basic components of ice skating and a balanced content of the program. Athletes are tasked with demonstrating possession of all groups of elements - steps, spirals, spins, jumps. In overcoming these difficulties, a mathematical model can significantly help, which allows you to select various parameters for the more successful execution of the elements of figure skating, taking into account the individual parameters of the skaters and without unnecessary physical costs.