Accelerometers used in the measurement of jerk, snap, and crackle

摘要

Accelerometers are traditionally used in acoustics for the measurement of vibration. Higher derivatives of motion are rarely considered when measuring vibration. This paper presents a novel usage of a triaxial accelerometer to measure acceleration and use these data to explain jerk and higher derivatives of motion. We are all familiar with the terms displacement, velocity and acceleration but few of us are familiar with the term jerk and even fewer of us are familiar with the terms snap and crackle. We experience velocity when we are displaced with respect to time and acceleration when we change our velocity. We do not feel velocity, but rather the change of velocity i.e. acceleration which is brought about by the force exerted on our body. Similarly, we feel jerk and higher derivatives when the force on our body experiences changes abruptly with respect to time. The results from a gymnastic trampolinist where the acceleration data were collected at 100 Hz using a device attached to the chest are presented and discussed. In particular the higher derivates of the Force total equation are extended and discussed, namely: i_(jerk)·d~3x/dt~3, r_(snap)·d~4x/dt~4, n_(crackle)·d~5x/dt~5 etc.