Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
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condition of zero angular velocity – changing from positive to negative – but to
a negative acceleration.
Points of inflexion
To interpret these, consider the positive and negative curvatures of the angle–time series
of Figure 3.22 and the point at which they meet. If the curvature is positive, the
gradient of the angle curve and, therefore, the angular velocity, is increasing. The
acceleration must, therefore, be positive for this portion of the curve. For an angle–time
curve, a positive curvature is a region of positive acceleration, reflecting an increasing
angular velocity. If the curvature is negative, so is the acceleration, and the gradient of
the angle–time curve – the angular velocity – is decreasing. The points of inflexion, F to
I, in Figure 3.22 indicate instances of zero acceleration.
Stationary points of inflexion
A point of inflexion at which the gradient of the tangent happens to be zero fulfils the
conditions of a stationary point, which is why it is called a stationary point of inflexion.
It does not fulfil the extra condition required for a turning point; that the slope changes
sign. These are rarely encountered by human movement analysts.