Scientific paper ID 2123 : 2021/3 STUDY THE TRAJECTORIES OF A TENNIS BALLAnastas Ivanov Ivanov Modern tennis sport is characterized by constant change in several directions. The most significant of these changes are connected to the design of tennis rackets. The composite material of the rocket’s frame is continuously improved. It is also working hard on improving the tennis strings. Tennis balls are also being modified. All these innovations lead to a change in the shot technique of the athletes. Modern tennis players use a variety of strokes. From the physical point of view, these blows can be classified into eight main groups depending on the way the racket interacts with the tennis ball. These are the strokes with top, bottom, side, top-side, and bottom-side rotation, as well as strokes without rotation. These eight interactions lead to main types of trajectories at the same initial position and the same initial linear velocity. The main purpose of the work is to study the two most important strokes in professional tennis: forehand with upper rotation and backhand with lower rotation. The calculations and graphical images are performed with the MatLab mathematical package. The conclusions are important not only for specialists in the field of Theoretical and Applied Mechanics, but they would also be useful for sports specialists, coaches, and tennis players. траектории тенис топка удари с ротация ефект на Магнус числено решение MatLabtrajectories tennis ball strokes with rotations Magnus effect numerical solution MatLabAnastas Ivanov IvanovBIBLIOGRAPHY[1] Cross R. Dynamics properties of tennis balls. Physics Department, Sport Engineering, 2, 1999, pp. 23-33. [2] Cooke, A.J., An overview of tennis ball aerodynamics. Sport Engineering, 3 (2), 2000, pp. 123-129. ( [2] Cooke, A.J., An overview of tennis ball aerodynamics. Spоrt Engineering, 3 (2), 2000, pp. 123-129. )[3] Mehta R.D., Pallis J.M., Sports ball aerodynamics: effects of velocity spin and surface roughness. Materials and Science in Sports, TMS, 2001, pp. 185-197. [4] Chadwick S.G., The aerodynamics properties of tennis balls. The University of Sheffield, Department of Mechanical Engineering, PhD dissertation, 2003, p. 331. [5] Gonzales O., Graf A.B., Maddocks J.H., Dynamics of rigid body in a Stockes fluid, Jour. Fl. Mech., 519, Cambridge, DOI: 10.1017/S0022112004001284, 2004, pp 133-160 [6] Cohen C., Clanet C., Physics of Ball Sports. EPN 47/3, 2016, pp. 13-16, doi: http://dx.doi.org/10.1051/epn/2016301. [7] Li F., Liu L., Wang Q., Qin K., Hu Q., Yang Q., Liu Y., Zhang B., Tennis balls judgment model based on numerical simulation. National Convention on Sports Sc. Of Cina, 01018, 2017, pp. 1-3, doi: 10.1051/ncssc/201701018. [8] Kwon S., Pfister R., Hager R.L., Hunter I., Steely M.K., Influence of tennis racquet kinetics of ball topspin angular velocity and accuracy during the forehand grandstroke. Journal of Sports Science and Medicine, 16, 2017, pp. 505-513. [9] Landlinder J., Lindiger S.J., Stöggl T., Wagner H., Müller E., Kinematic differences of elite and high-performance tennis players in the cross court and down the line forehand. Sport Biomechanics, 9 (4), 2010, pp. 280-285. [10] Ivančević T., Jovanović B., Dikić M., Marković S., Dukić N., Biomechanical analysis of shots and ball motion in tennis and analogy with handball throws. Facta universitatis, series: Physical Education and Sport, vol. 6, № 1, 2008, pp. 51-66. [11] Alam F., Subic A., Naser J., Rasul M.G., Khan M.M.K., A sydy of sin efects on tennis ball aerodynamics. WSEAS Transactions on Fluid Mechanics, vol. 3. Issue 3, ISSN: 1790- 5087, 2008, pp. 271-278. [12] Chadwick S.G., Haake S.J., The drag coefficient of tennis balls. Engineering of Sport Conference, Sydney, June 2000, pp. 169-176. [13] Goodwill S.R., Chin S.B., Haake S.I., Aerodynamics of spinning and non-spinning tennis balls. Journ. Wind Eng. and Indust. Aerodyn. vol. 92, Issue 11, 2004, pp. 935-958. [14] Mehta R., Alam F., Subic A., Review of tennis ball aerodynamics. Sports Technology, No 1, John Wiley and Sons Asia Pte Ltd, 2008, pp. 1-16, doi: 10.1002/jst.11. [15] Nakajima T., Hiratsuka M., Ito S., Konno A., Aerodynamics characteristics and PIV analyses concerning tennis balls. IOP Conf. Series: Materials Sciene and Engineering 249, 012021, 2017, pp. 1-4. [16] Cross R., Londsey C., Masurements of drag and lift on tennis balls in flight. Sports Engineering 17 (2), doi: 10.1007/s12283-013-0144-9, 2013, pp. 89-96. [17] Cross R., Calculations of groundstroke trajectories in tennis. School of Physics, University of Sydney, 2020, pp.1-20, doi: 10.1007/s12283-020-00322-1. [18] Ivanov A.I., Three-dimensional study of tennis ball flight. Journal Mechanics of Machines, year XXII, book 2, ISSN 0861-9727, 2014, pp. 34-37.

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