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Absity-tan (ID: !UI10xzyueI)
Absity and Absement: Are Further Integrals Practical and Able to Be Understood by Mortals? 2016-11-17 05:43:11 Post No. 8479402
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Absity and Absement: Are Further Integrals Practical and Able to Be Understood by Mortals? 2016-11-17 05:43:11 Post No. 8479402
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Absity and Absement: Are Further Integrals Practical and Able to Be Understood by Mortals?
Absity-tan (ID: !UI10xzyueI)
2016-11-17 05:43:11
Post No. 8479402
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Physics/Calculusbros please help me understand this concept:
Absement is the integral of displacement, expressed in units of meterseconds (absement is found using the equation A=ms). Absement is essentially a measure of both how long a point/object was at its position and for how long.
For instance, imagine you have a cell service that charges you based on how far you are from their cell tower multiplied by how long you use the phone. A= m(how far you are) x s(how long the phone is used), and then they would probably the value by whatever constant they use to determine price.
In a scenario of absement, distance and time are multiplied, rather than divided, which is the main difference between displacement's integrals, which I will call the "negatve" vectors, and displacement and it's derivatives, which I will call the "positive" vectors, respectively.
However, I am having a hard time conceptualizing absity, or the integral of absement, mostly because I don't see the "linking mechanic" that links the negative vectors. For the positive vectors, it's the rate of change, i.e. velocity is HOW FAST an object's displacement changes and acceleration is HOW FAST an object's speed changes, so on and so forth.
The above makes sense because we are taking the previous degree and giving it a further rate of change relative to time (1/s).
I cannot conceptualize the idea of decreasing the rate of change. Perhaps the first step would be someone explaining the relationship of a derivative of position and it's integral, in that order (for instance, the relationship between acceleration and velocity).
tl;dr please help me understand the 2nd integral of position, absity. It has been plaguing my mind for literally 5 years and I just want to understand it.
pic is absement btw, not absity.
(CONT.)
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Oh I didn't mean to add the (CONT.) thing to the end of the post.
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it is pretty much a non physical idea. It emerges out of the mathematics and has, I would venture to say, extremely limited if any, physical significance.
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>>8479444
but it must at least still have a conceptualization
i can explain that the 3rd derivative of displacement, jerk, is how fast the acceleration changes, and can be applied in rollercoaster construction, for instance, to make sure the riders don't suffer from whiplash by the ride accelerating too quickly
even though I can't find an application for the 4th derivative, jounce, I can still understand it as "how fast the degree of 'jerk' changes". I can repeat this ad infinatum in the "positive" direction, but I can not even relate absement to its integral.
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bump
please help me
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Let's think... so displacement is the integral of velocity, which is where were you when you were going at such velocity. In the same spirit velocity is how fast you were going when you had such acceleration.
Now the integral of where you are right now is ... how long you were at a certain place?
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>>8479451
Jounce and higher are used in quadcopter control, as they are useful stability mode measurements
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Think of integrals and derivatives as "functions" of functions that relate a function to another. In this case all those functions are related to speed, displacement, etc.
Acceleration changes the direction of displacement and such.
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>>8479402
Could be used for absement for a PI or PID controller.
Something like an inverted pendulum, but that's really angular absement.
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>>8480595
maybe I'm retarded but I don't understand any of that
what is a PI/PID controller? inverted pendulum?
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bump
please help me someone
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>>8480546 this made think of something like average weighted position - the integral of position would add up each time point, weighted by the position at each time point. If it was a definite integral, the weighted position would end up at a certain value which represents how the much the "scale" has tipped toward positive or negative during the time period.
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>>8482915
explain
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>>8480596
Proportional-Integral Controller, the D is for if there's a derivative term.
You take an unstable system like an inverted pendulum on a cart. (look up a video)
You apply a force proportional to the angle offset from the unstable equillibrium point (straight up). A stronger controller could have an integral term, which would just be (angular) absessment multiplied by a new proportional constant
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