Skip to main content
SpringerLink
Log in

Acceleration helps in skateboarding at high speeds

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

The aim of this study is to investigate the dynamics of an accelerating skater–board system modeling downhill motion. The governing mathematical model is a system of time-varying neutral delay-differential equations. Stability analysis is performed based on the frozen-time method, and the results are verified via numerical simulations. It is shown that the varying longitudinal speed may result in loss of stability at high speeds, which explains the unpredictable falling often observed at real downhill skateboarding. The positive effect of large longitudinal acceleration on the stability is also demonstrated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Hubbard M (1979) Lateral dynamics and stability of the skateboard. J Appl Mech 46:931–936. https://doi.org/10.1115/1.3424680

    Article  Google Scholar 

  2. Hubbard M (1980) Human control of the skateboard. J Biomech 13(9):745–754. https://doi.org/10.1016/0021-9290(80)90236-5

    Article  Google Scholar 

  3. Bloch AM (2003) Nonholonomic mechanics and control. Springer, New York

    Book  Google Scholar 

  4. Stepan G (2009) Delay effects in the human sensory system during balancing. Philos Trans R Soc Lond A Math Phys Eng Sci 367(1891):1195–1212

    Article  MathSciNet  MATH  Google Scholar 

  5. Insperger T, Milton J (2014) Sensory uncertainty and stick balancing at the fingertip. Biol Cybern 108(1):85–101. https://doi.org/10.1007/s00422-013-0582-2

    Article  MathSciNet  MATH  Google Scholar 

  6. Chagdes JR, Rietdyk S, Jeffrey MH, Howard NZ, Raman A (2013) Dynamic stability of a human standing on a balance board. J Biomech 46(15):2593–2602. https://doi.org/10.1016/j.jbiomech.2013.08.012

    Article  Google Scholar 

  7. Kremnev AV (2008) Dynamics and simulation of the simplest model of a skateboard. In: Proceedings of Europian nonlinear dynamics conference 2008 (ENOC-2008), 30 June–4 July, 2008, Saint Petersburg, Russia

  8. Varszegi B, Takacs D (2016) Downhill motion of the skater–skateboard system. Period Polytechn Mech Eng 60(1):58–65. https://doi.org/10.3311/PPme.8636

    Article  Google Scholar 

  9. Rosatello M, Dion JL, Renaud F, Garibaldi L (2015) The skateboard speed wobble. In: Proceedings of ASME 11th international conference on multibody systems, nonlinear dynamics, and control, 2–5 Aug 2015, Boston, MA, USA. https://doi.org/10.1115/DETC2015-47326

  10. Varszegi B, Takacs D, Stepan G, Hogan SJ (2016) Stabilizing skateboard speed-wobble with reflex delay. J R Soc Interface 13:20160345. https://doi.org/10.1098/rsif.2016.034

    Article  Google Scholar 

  11. Wisse M, Schwab AL (2005) Skateboards, bicycles, and three-dimensional biped walking machines: velocity-dependent stability by means of lean-to-yaw coupling. Int J Robot Res 24(6):417–429. https://doi.org/10.1177/0278364905053803

    Article  Google Scholar 

  12. Collins S, Ruina A, Tedrake R, Wisse M (2005) Efficient bipedal robots based on passive-dynamic walkers. Science 307(5712):1082–1085. https://doi.org/10.1126/science.1107799

    Article  Google Scholar 

  13. Cossalter V, Lot R, Massaro M (2008) The chatter of racing motorcycles. Veh Syst Dyn 46(4):339–353. https://doi.org/10.1080/00423110701416501

    Article  Google Scholar 

  14. Weiss L, Infante E (1965) On the stability of systems defined over a finite time interval. Proc Nat Acad Sci 54(1):44–48

    Article  MathSciNet  MATH  Google Scholar 

  15. Moulay E, Perruquetti W (2008) Finite time stability conditions for non-autonomous continuous systems. Int J Control 81(5):797–803. https://doi.org/10.1080/00207170701650303

    Article  MathSciNet  MATH  Google Scholar 

  16. Peterka RJ (2002) Sensorimotor integration in human postural control. J Neurophysiol 88(3):1097–1118. https://doi.org/10.1152/jn.00605.2001

    Article  Google Scholar 

  17. Kane TR, Levinson DA (2005) Dynamics, theory and applications. Internet-First University Press, Ithaca

    Google Scholar 

  18. Baruh H (1999) Analytical dynamics. WCB/McGraw-Hill, Boston

    Google Scholar 

  19. Insperger T, Stepan G (2011) Semi-discretization for time-delay systems–stability and engineering applications. Springer, New York

    Book  MATH  Google Scholar 

  20. Loram ID, Lakie M (2002) Direct measurement of human ankle stiffness during quiet standing: the intrinsic mechanical stiffness is insufficient for stability. J Physiol 545(3):1041–1053. https://doi.org/10.1113/jphysiol.2002.025049

    Article  Google Scholar 

  21. Stepan G (1989) Retarded dynamical systems: stability and characteristic functions. Longman Scientific, London (UK & Technical co-published with Wiley, New York)

    MATH  Google Scholar 

  22. Guiness World Records (Online). http://www.guinnessworldrecords.com/. Accessed 18th July 2017

  23. Varszegi B, Takacs D, Stepan G (2017) Stability of damped skateboards under human control. J Comput Nonlinear Dyn 12(5):051014. https://doi.org/10.1115/1.4036482

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Balazs Varszegi & Tamas Insperger

  2. MTA-BME Lendulet Human Balancing Research Group, Budapest, Hungary

    Balazs Varszegi & Tamas Insperger

  3. MTA-BME Research Group on Dynamics of Machines and Vehicles, Budapest, Hungary

    Denes Takacs

Authors
  1. Balazs Varszegi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Denes Takacs
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tamas Insperger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Balazs Varszegi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Varszegi, B., Takacs, D. & Insperger, T. Acceleration helps in skateboarding at high speeds. Int. J. Dynam. Control 6, 982–989 (2018). https://doi.org/10.1007/s40435-017-0368-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-017-0368-9

Keywords

Search

Navigation