*3.6. Jerk in GPS Applications*

The following articles discussed use of jerk in Global Positioning Systems (GPS), mainly those types that should perform in harsh dynamic conditions such as satellite launch vehicles (Table 10).

#### *3.7. Jerk in Human Tolerance*

Details of works studying human tolerance to jerk are given in Table 11.

#### *3.8. Jerk In Kinesiology*

Jerk has been used in different kinesiologies in different fields of clinical studies in sport science. Below, those works which studied jerk in kinesiology for different applications [139–147] have been captured (Table 12).

Recently, jerk has gained interest in non-clinical trials. For instance, in a recent study by Zhang [145–147], jerk was used as a measure to detect fatigue in workers.

#### *3.9. Jerk in Measurement*

Jerk is normally measured indirectly by calculating the derivative of acceleration, which is measured by accelerometers. Below, those studies that developed a device to measure jerk are tabulated (Table 13).

#### *3.10. Jerk in Motion Analysis*

In motion analysis application, jerk is used as s measure in machine learning classifiers [152,153] (Table 14).

#### *3.11. Jerk in Ornithology*

Ornithology is a branch of zoology which deals with birds. jerk has been used in one of the recent studies in this area, details of which are given in Table 15.

#### *3.12. Jerk in Greyhound Racing*

One of the interesting applications (refer to Table 16) of jerk is in high-speed sprint racing, such as greyhound racing. Recent articles on racing greyhounds, mainly the one in Nature's Scientific Report [160], clearly show its importance.

#### *3.13. Jerk in Sea-Keeping*

Jerk in sea-keeping is considered in both passengers' ride comfort and analysing shock spectrum in high-speed crafts [8–10,122,126,204] (Table 17).



*Vibration* **2020**, *3*



**Table8.***Cont.*




 *3* medicine

occur. Jerk was referred to as

acceleration

 onset rate.



**Table12.**Jerkinkinesiology.



**Table 13.** Jerk in measurement.


recommended

 safe jerk limit (for

than the

birds).

humans/no

 data for

captured

jerk should be considered

such scenarios.

 by

acceleration

 and

 in

*Vibration* **2020**, *3*


**Table 16.** Jerk in greyhound racing.


**Table17.**Jerkinsea-keeping.

### *3.14. Jerk in Seismic Analysis*

Seismic analysis is a subset of structural analysis and is the calculation of the response of a building structure to earthquakes. It is part of the process of structural design, earthquake engineering or structural assessment and retrofit in regions where earthquakes are prevalent [134,161–170] (Table 18).

## *3.15. Jerk in Shock Response Spectrum*

Equipment that is delivered to naval ships needs to be shockproof. The basic philosophy is that the equipment should withstand the same explosions as the ship itself (it would be unfortunate if the ship survived the blast, while it were impossible to operate since all equipment has been destroyed). Preferably, the shock-proofness of the equipment should be verified both theoretically and experimentally.

There are essentially three methods for theoretical verification, including:


Static calculations are easiest to carry out. In these calculations, neither the shape of the time history of the shock (e.g., blast or earthquake) nor the dynamic properties of the equipment under consideration (e.g., resonance frequencies) are taken into account. This means that you should normally have a considerable safety margin.

The shock response spectrum was invented by the Flemish-American engineer Maurice Anthony Binot (1905–1985). The basic idea is to draw a diagram that shows the maximum acceleration and relative displacement for a number of single-mass oscillators with various eigen frequencies for a certain shock time history. Normally, a simplified curve is drawn that might be an envelope for several time histories. This curve can be used to calculate the maximum amplitude for each eigenmode of the real equipment, and finally the contributions of each eigenmode can be added. There are different ways to add the contributions from the eigenmodes depending on how cautious you are. The very conservative approach is that you assume that, at some point in time, all the contributions of the eigenmodes are pointing in the same direction. This curve can not be used for testing, so a new time history curve has to be synthesised as input to that activity. It is out of the scope of this article to discuss details of this method, but it is interesting to point out that in these calculations jerk, etc., are implicitly taken into account.

The most straightforward method to carry out shock calculations is by integration in the time domain. Since the calculations are based on the time history, the derivatives of the acceleration are implicitly taken into account. The time history can, of course, directly be used as input to the test activity and comparison between calculations and measurements should be straightforward. The main drawback of this method is that it consumes a lot of computer power.

Studies that studied jerk in shock responses are listed in Table 19.

#### *3.16. Jerk in Sport Science*

Sport science is a general term which can include the science behind designing running shoes and studying the impact attenuation properties of greyhound's surface. Those articles that passed the inclusion criteria of this work are tabulated in Table 20.

#### *3.17. Jerk in Structural Health Monitoring*

Vibration monitoring is another challenging area, e.g., it would be beneficial to be able to be able to identify the wear on gearboxes of wind power stations in due time. However, the application of higher-order derivatives of acceleration for damage detection requires further investigation. Using jerk as one parameter to be monitored has been suggested, e.g., by Zhang et al. (2012) [174] (Table 21).



**Table 18.** Jerk in seismic analysis.






