TABLE 1.

Several Jerk-Based Measures of Movement Smoothness and Their Dimensions

Measure	Formula	Dimensions	Study
Integrated squared jerk	${\int }_{t_1}^{t_2}\stackrel{\dots }{x}{(t)}^{2}dt$	$\frac{L^2}{T^5}$	Platz, Denzler, Kaden, & Mauritz (1994)
Mean squared jerk	$\frac{1}{t_2-t_1}{\int }_{t_1}^{t_2}\stackrel{\dots }{x}{(t)}^{2}dt$	$\frac{L^2}{T^6}$	Wininger, Kim, & Craelius (2009)
Cumulative squared jerk	${\sum }_{k=1}^n\stackrel{\dots }{x}{(t_k)}^2$	$\frac{L^2}{T^6}$	Smith, Brandt, & Shadmehr (2000)
Root mean squared jerk	$\sqrt{\frac{1}{t_2-t_1}{\int }_{t_1}^{t_2}\stackrel{\dots }{x}{(t)}^{2}dt}$	$\frac{L}{T^3}$	Young & Marteniuk (1997)
Mean squared jerk normalized by peak speed	$\frac{1}{v_{\mathit{peak}}(t_2-t_1)}{\int }_{t_1}^{t_2}\stackrel{\dots }{x}{(t)}^{2}dt$	$\frac{L}{T^5}$	Hester et al. (2006)
Integrated absolute jerk	${\int }_{t_1}^{t_2}|\stackrel{\dots }{x}(t)|dt$	$\frac{L}{T^2}$	Goldvasser, McGibbon, & Krebs (2001)
Mean absolute jerk normalized by peak speed	$\frac{1}{v_{\mathit{peak}}(t_2-t_1)}{\int }_{t_1}^{t_2}|\stackrel{\dots }{x}(t)|dt$	$\frac{1}{T^2}$	Rohrer et al. (2002)

Note. L = length; T = time; t_k = discrete samples.