The Skier as an Inverted Pendulum

  • David A. Lind
  • Scott P. Sanders


Let us model the skier on the slope as a system assumed to be a pendulum inverted on its pivot point as shown in Fig. T11.1 [1]. The ski acts as the pivot point, and it may move sideways or be fixed by edging; in either case the ski provides the necessary vertical and transverse forces to make it the pivot point in our model. The rigid connection between the leg, the boot, and the ski provides stability fore and aft. The reaction force R balances the weight Mg, mass times the acceleration of gravity; the lateral force at the pivot point F balances the inertial force, Mÿ.


Tilt Angle Lateral Force Inverted Pendulum Pivot Point Bank Angle 
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  1. 1.
    This discussion is indebted to J. M. Morawski’s article, “Control Systems Approach to a Ski-Turn Analysis,” J. Biomech. 6, 267 (1973). Morawski uses γ to refer to the tilt angle in his “skier as pendulum” discussion, and we use Morawski’s notation for the tilt angle here. Readers should note that in our preceding discussions of turning on skis in the main body of the book and in other Technotes, this tilt angle has been noted as φ.Google Scholar

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© Springer Science+Business Media New York 2004

Authors and Affiliations

  • David A. Lind
    • 1
  • Scott P. Sanders
    • 2
  1. 1.University of ColoradoBoulderUSA
  2. 2.University of New MexicoAlbuquerqueUSA

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