Document Type : Research Paper


1 Assistant Professor of Sports Biomechanics. Kharazmi University

2 Professor of Sports Biomechanics, Kharazmi University

3 Assistant Professor of Mechanical Engineering, Kharazmi University


Quantifying dynamic stability of athletic skills help to identification of motor behavior complexity to reduce injury and improve performance. The purpose of this study was to evaluate the effects of training on local dynamic stability in vertical jump maneuver. Twenty young male subjects (control (n=10), exercise (n=10)) participated in this study. Hip and knee kinematics and ground reaction forces data during vertical jump were recorded at pre-test and post-test. Exercise group participated in the vertical jump training program for four weeks (Twelve 40-minute sessions). Using largest finite- time Lyapunov exponent; a nonlinear method; local dynamic stability of hip and knee angular positions was calculated. The results showed that following increase in vertical jump height, selected protocol training significantly improved the dynamical stability of the knee joint. It seems, increasing vertical jump height following training, leading to greater stability of the knee joint rather than the hip.


1. Tomika M, Owings T M, Grabiner M D. Lower extremity strength and coordination are independent contributors to maximum vertical jump height. J Appl Biomech. 2001; 17: 181-7.
2. Bobbert M, Van Soest A J. Why do people jump the way they do? Exer Sport Sci. 2001; 29: 95-102.
3. Harrison A, Ryan W, Hayes K. Functional data analysis of joint coordination in the development of vertical jump perfomance. Sport Biomech. 2007; 6: 199-214.
4. Hasson C, Dugan E L, Doyle T L, Humphries B, Newton R U. Neuromuscular strategies employed to increase jump height during the initiation of the squat jump. J Electromyogr Kinsiol. 2004; 14: 515-21.
5. Miller D, East D J. Kinematic and kinetic correlates of vertical jumping in women. Biomechanics, University Park Press, Baltimore. 1976; P. 65-72.
6. Prilutsky B, Zatsiorsky V M. Tendon action of two-joint muscles: Transfer of mechanical energy between joints during jumping, landing and runing. J Biomech. 1994; 27: 25-34.
7. Temfemo A, Hugues J, Chardon K, Mandengue Sh, Ahmaidi S. Relationship between vertical jumping performance and anthropometric charactristics growth in boys and girls. Eur J Pediatr. 2009; 168: 457-64.
8. Panoutskopoulos V, Papachatzis N, Kollias I A. Sport specifity background affects the principal component structure of vertical jump performance of identifying performance enhancement interventions. J of Sport & Healt Sci. 2014; 3(3): 239-47.
9. Park G. The use of intra-subject variability as a means of identifying performance. Master thesis. School of Healt and Human Performance, Dublin City University; 2005.
10. Dowelling J J, Vamos L. Identification of kinetic and temoral factors related to vertical jump performance. J of Appl Biomech. 1993; 9(2); 95-110.
11. Hochmuth G. Biomechanics of athletic movement. Berlin: Sportverlag; 1st ed. 1984. P.171-9.
12. Jaric S, Ristanovic D, Corcos D M. The relationship between muscle kinetic parameters and kinematic variables in a complex movement. Eurpo J of Appl Physiol & Occup Physiol. 1989; 59(5): 370-6.
13. Oddsson L. What factors determine vertical jumping height? 5th International Symposium on Biomechanics in Sports. Athens, Greece, 1987. 393-401.
14. Robertson D, Fleming D. Kintics of standing broad and vertical jumping. Can J Sport Sci. 1987; 12(1): 19-23.
15. Stergiou N. Innovative analysis of human movement. Champaign IL: Human Kinetic; 1st ed. 2004. p. 29-87.
16. Kang H G. Kinematic and motor variability and stability during gait: Effects of age, walking speed and segment height. Doctoral thesis. The University of Texas at Austin; 2007.
17. James C R, Bates B T, Dufek J S. Classification and comparison of biomechanical response strategies for accommodating landing impact. J of Appl Biomech. 2003; 106-18.
18. Salaj S S, Milanovic D, Jukic I. The effects of proprioceptive training on jumping and agility performance. Kinesiol. 2007; 39(2): 134-41.
19. McBride J M, Triplett McBride T, Davie A, Newton R U. The effect of heavy vs. light-load jump squats on the develoment of strenght, power, and speed. The J of Stren & Cond Res. 2002; 16(1): 82-75.
20. Newton R U, Rogers R A, Volek J S, Hakkinen K, Kraemer W J. Four weeks of optimal load ballistic resistance training at the end of saeson attenuates declining jump performance of women volleyball players. The J of Streng & Cond Res. 2006; 20(4): 955-61.
21. Sheppard J M, Dingley A A, Janssen I, Sprotford W, Chapman D W, Newton R U. The effect of assisted jumping on vertical jump height in high-performance volleyball players. J of Sci & Med in Sport. 2001; 14(1): 85-9.
22. Bernstein N A. Dexterity and its development. Psychology Press; Taylor & Francis Group. New York. 1st ed. 1996. P. 305-39.
23. Karver A A. Sand jump training versus ground jump training for volleyball players. Master thesis; California State University, Sacramento. 2012.
24. Bobbert M F, Gerritsen K G, Litjens M C, Van Soest A J. Why is countermovement jump height greater than squat jump height? Med & Sci in Sports & Exe. 1996; 28: 1402-12.
25. Arabatzi F, Kellis E, De Villarreal E S. Vertical jump biomechanics after plyometric, weight lifting, and combined (weight lifting+ plyometric) training. The J of Streng & Cond Res. 2010; 24(9): 2440-8.
26. De Villarreal E S, Kellis E, Kraemer W J., Izquierdo M. Determining variables of plyometric training for improving vertical jump height performance: A meta-analysis. The J of Streng & Cond Res. 2009; 23(2): 495-506.
27. Faigenbaum A D, McFarland J E, Keiper F B, Tevlin W, Ratamess N A, Kang J. Effects of a short-term plyometric and resistance training program on fitness performance in boys age 12 to 15 years. J of Sports Sci & Med. 2007; 23(2): 495-506.
28. Kotzamanidis C. Effect of plyometric training on running performance and vertical jumping in prepubertal boys. The J of Streng & Cond Res. 2006; 20(2): 441-5.
29. Kubo K, Morimoto M, Komuro T, Yata H, Tsunoda N, Kanehisa H. Effects of plyometric and weight training on muscle-tendon complex and jump performance. Medicine & Sci in Sports & Exe. 2007; 39(10): 1801-10.
30. Cavanaugh J T, Guskiewicz K M, Stergiou N. A nonlinear dynamic approach for evaluating postural control: New directions for the management of sport-related cerebral concussion. Sport Med. 2005; 35: 935–50.
31. Abarbanel H D I. Analysis of observed choatic data. New York: Springer-Verlag; 1st ed. 1996. P.13-65.
32. Dingwell J B, Cusumano J P. Nonlinear time series analysis of normal and pathological human walking. Chaos. 2000; 10: 848-63.
33. Rapp P E. A guide to dynamical analysis. Integ Physiol & Behav Sci. 1994; 29: 311-27.
34. Wolf A, Swift J B, Swinney H, Vastano J A. Determining lyapanov exponents from a time series. Physica D. 1985; 284-311.
35. Nayfeh A H. Applied nonlinear dynamics: Analytical, computational, and experimental methods. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim; 1st ed. 2004. P. 461-557.
36. Strogatz Sh. Nonlinear dynamics and chaos. Cambridge, MA, USA: Perseus Books Publishing; 2th ed. 2000. P.76-145.
37. Ratcliffe R J, Holt K G. Low frequency shock absorption in human walking. Gait & Post. 1997; 5(2): 93-100.
38. Cromwell R, Schurter J. Head stabilization strategies in the sagittal plane during locomotor tasks. Physiother Res Int. 2004; 9(1): 33-42.
39. Granata K P, Lockhart T E. Group differences among fall-prone individuals and healthy old and younger counterparts utilizing nonlinear stability measures. J of Biomech. 2006; 39(1): 81-9.
40. Demura S, Kitabayashi T, Aoki H. Body-sway characteristics during a static upright posture in the elderly. Geriat & Gerontol Internat. 2008; 8: 188–97.
41. Cavanaugh J T, Guskiewicz K M, Stergiou N. A nonlinear dynamic approach for evaluating postural control: New directions for the management of sport-related cerebral concussion. Sport Med. 2005; 35: 935–50.
42. Li L, Haddad J M, Hamill J. (2005). Stability and variability may respond differently to changes in walking speed. Hum Move Sci. 2005; 24: 257-67.