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In kinematics, absement is a measure of sustained displacement of an object from its initial position, i.e. a measure of how far away and for how long. The word absement is a portmanteau of the words absence and displacement.
Absement changes as an object remains displaced and stays constant as the object resides at the initial position. It is the first time-integral of the displacement (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement. The dimension of absement is length multiplied by time. Its SI unit is meter second (m·s), which corresponds to an object having been displaced by 1 meter for 1 second. This is not to be confused with a meter per second (m/s), a unit of velocity, the time-derivative of position.
For example, opening the gate of a gate valve (of rectangular cross section) by 1 mm for 10 seconds yields the same absement of 10 mm·s as opening it by 5 mm for 2 seconds. The amount of water having flowed through it is linearly proportional to the absement of the gate, so it is also the same in both cases.Maya Burhanpurkar. Absement: Direct Evidence of the Time-Integral of Distance. Canada-Wide Science Fair 2014.
The first published paper on the topic of absement introduced and motivated it as a way to study
flow-based musical instruments, such as the hydraulophone, to model empirical observations of some hydraulophones in which obstruction of a water jet for a longer period of time resulted in a buildup in Loudness, as water accumulates in a sounding mechanism (reservoir), up to a certain maximum filling point beyond which the sound level reached a maximum, or fell off (along with a slow decay when a water jet was unblocked). Absement has also been used to model artificial muscles,ROBUST CONTROL LAW FOR PNEUMATIC ARTIFICIAL MUSCLES, Jonathon E. Slightam and Mark L. Nagurka, Proceedings of the ASME/Bath 2017 Symposium on Fluid Power and Motion Control, FPMC 2017, October 16–19, 2017, Sarasota, USA as well as for real muscle interaction in a physical fitness context.Effectiveness of Integral Kinesiology Feedback
for Fitness-based Games, Steve Mann, Max Lv Hao, Ming-Chang Tsai, Maziar Hafezi, Amin Azad, and Farhad Keramatimoezabad, 2018 IEEE Games, Entertainment, Media Conference (GEM), pages 43-50 Absement has also been used to model human posture.Postural strategy for mediolateral weight shifting in healthy adult, J Tousignant, C Cherriere, A Pouliot-Laforte, É Auvinet, Gait & Posture, 2018 - Elsevier
As the displacement can be seen as a mechanical analogue of electric charge, the absement can be seen as a mechanical analogue of the time-integrated charge, a quantity useful for modelling some types of memory elements.
Building on the concept of anglement, "Einstein's Lane Method" could be used to describe the spatiotemporal trajectory of systems involving rotational motion or angular displacement. Einstein’s Lane Method provides a framework for analyzing the curved paths of rotating objects or systems under the influence of gravitational fields, similar to how general relativity describes the bending of spacetime. This method would use angular displacements (rather than linear positions) as key variables, integrating them over time, much like the time-integral of angle in anglement.
This is consistent with Jeltsema's 2012 treatment with charge and flux as the base units rather than current and voltage.
Applications
In addition to modeling fluid flow and for Lagrangian modeling of electric circuits, absement is used in physical fitness and kinesiology to model muscle bandwidth, and as a new form of physical fitness training."Integral Kinematics (Time-Integrals of Distance, Energy, etc.) and Integral Kinesiology", by Mann etal, in Proceedings of the IEEE GEM 2014, pp. 270-2. In this context, it gives rise to a new quantity called actergy, which is to energy as energy is to power. Actergy has the same units as action (joule-seconds) but is the time-integral of total energy (time-integral of the Hamiltonian rather than time-integral of the Lagrangian).
Just as displacement and its derivatives form kinematics, so do displacement and its integrals form "integral kinematics".
Relation to PID controllers
are controllers that work on a signal that is proportional to a physical quantity (e.g. displacement, proportional to position) and its integral(s) and derivative(s), thusly defining PID in the context of integrals and derivatives of a position of a control element in the Bratland sense:
Strain absement
Strain absement is the time-integral of strain, and is used extensively in mechanical systems and memsprings. As Pei et al. describe:
Anglement
Absement originally arose in situations involving valves and fluid flow, for which the opening of a valve was by a long, T-shaped handle, which actually varied in angle rather than position. The time-integral of angle is called "anglement" and it is approximately equal or proportional to absement for small angles, because the sine of an angle is approximately equal to the angle for small angles.Integral Kinesiology Feedbackfor Weight and Resistance Training, 2019 15th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), http://wearcam.org/sitis2019.pdf
Phase space: Absement and momentement
In regard to a conjugate variable for absement, the time-integral of momentum, known as momentement, has been proposed.Mann, S., Janzen, R., Ali, M. A., Scourboutakos, P., & Guleria, N. (2014, October). Integral kinematics (time-integrals of distance, energy, etc.) and integral kinesiology. In Proceedings of the 2014 IEEE Games, Entertainment, Media Conference (GEM), Toronto, ON, Canada (pp. 22-24).Mann, S., Defaz, D., Pierce, C., Lam, D., Stairs, J., Hermandez, J., ... & Mann, C. (2019, June). Keynote-Eye Itself as a Camera: Sensors, Integrity, and Trust. In The 5th ACM Workshop on Wearable Systems and Applications (pp. 1-2).Biolek, Z., Biolek, D., Biolková, V., & Kolka, Z. (2021). Lagrangian and Hamiltonian formalisms for coupled higher-order elements: theory, modeling, simulation. Nonlinear Dynamics, 1-14.Mann, S., Pierce, C., Zheng, B. C., Hernandez, J., Scavuzzo, C., & Mann, C. (2019, November). Integral kinesiology feedback for weight and resistance training. In 2019 15th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS) (pp. 319-326). IEEE.
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