- #1
lucerne
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I wish to know why and how does hysteresis occur from a purely mathematical perspective, using analytical functions and multivariable calculus. Thank you!
A mathematical explanation of hysteresis?
- Context: Graduate
- Thread starter lucerne
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SUMMARY
Hysteresis is mathematically explained through the analysis of cubic or higher degree odd dependencies in multivariable calculus. When examining the phase plane of y versus dy/dt, hysteresis manifests as a jump between branches when certain conditions are met, specifically when the central part of the graph is unstable. This phenomenon is not limited to one field; it appears in mechanical systems, digital electronics, elasticity, and electromagnetism. A purely mathematical perspective on hysteresis is insufficient without incorporating relevant physics concepts.
PREREQUISITES- Understanding of multivariable calculus
- Familiarity with phase plane analysis
- Knowledge of cubic functions and their properties
- Basic concepts in physics related to mechanical systems and electromagnetism
- Research the mathematical properties of cubic functions in dynamical systems
- Study phase plane analysis techniques in multivariable calculus
- Explore applications of hysteresis in mechanical systems and digital electronics
- Investigate the relationship between hysteresis and stability in physical systems
Students and professionals in mathematics, physics, and engineering, particularly those interested in the mathematical modeling of physical phenomena and systems exhibiting hysteresis.
- #2
Vanadium 50
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Since some phenomena and materials experience this and some don't, a "purely mathematical perspective" is impossible. Some physics will need to enter the problem.
- #3
HallsofIvy
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From a purely mathematical point of view, hysteresis results when there is a cubic (or higher degree odd) dependence. If, in the phase plane (y versus dy/dt) y has a cubic dependence on dy/dt and we have the central part (in red in the graph below) unstable, then as x approaches 2 from below, it jumps to the other blue branch, going from 2 up. But as we come back down, x will stay on that section until it gets down to x= -2 before it jumps to the branch. (The x-axis is vertical in this graph.)
- #4
Studiot
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Hysteresis refers to an number of unrelated physical phenomena (and to some related ones) in mechanical systems, digital electronics, elasticity, electromagnetism to name but a few.
So if you would like to tell us which area you referring to please?
So if you would like to tell us which area you referring to please?
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