KNES 300 Lecture 6: Linear kinematics
14 Feb 2017
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Very common condition in human motion: any time forces other than gravity act on body, for example: locomotion (ground reaction forces, cannot use projectile motion equations. Possible measurements: motion capture: measure position, force platforms: measure acceleration, difficult to measure velocity. Position: integral of velocity vs. time. Velocity: slope of position vs. time, integral of acceleration vs. time. Acceleration: slope of velocity vs. time. Predict future value of a function from its current value and its derivatives. Use more derivatives = make a more accurate prediction. Suppose our function is position and we only care about the first derivative: Central difference: short time into the future and the past, middle frames. Backward difference: only current position and the previous position, last frame. Gains in accuracy are negligible for the timestep sizes we use in modern motion analysis. In other words: first order differences are usually good enough. Important notes on numerical differentiation: estimating derivatives, error is proportional to timestep size.
