*Forma,* Vol. 16 (No. 1), pp. 17-46, 2001

*Original Paper*

## Mathematical Index and Model in Stabirometry

Hiroki Takada^{1}, Yoshiyuki Kitaoka^{2} and Yuuki Shimizu^{3}

^{1}Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan

^{2}Department of Mathematics, Meijo University, Tempaku-ku, Nagoya 468-8502, Japan

^{3}Institute for Hydrospheric-Atmospheric Sciences, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan

(Received April 20, 2000; Accepted March 21, 2001)

**Keywords: **
Sway of the Center-of-Gravity of the Body, Stabirometry, Fokker-Planck Equation (FPE), Stochastic Dynamical Equation (SDE), Form of a Potential Function

**Abstract. **
We measured the sway of the center-of-gravity of the body with a stabirometer for five men aged of 19 to 25 years. There are standardized parameters on stabirometry (observation with the stabirometer) by SUZUKI *et al*. (1996). We have analyzed the measured data by paying attention to *force* acting on it. We could admit *polarity* and *rhythm* on the force and the kind of effect of visual information. We also constructed a mathematical model of the sway of the center-of-gravity of the body on some conditions. We obtained a stochastic dynamical equation system as a mathematical model corresponding to the sway of the center-of-gravity of the body. We compared the statokinesigram obtained from the numerical simulation of this SDE with that obtained from the measured data.

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