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A 1st Order curve is a simple decay curve, like an electronic capacitor charging or discharging. It is a characteristic SHAPE. The math of it is incidental and depends upon the values of circuit components. That is; the amplitude of the measured variable is determined by the input charging value, and the decay rate is determined by system capacitance and output resistance.
Take for instance a nice hot cup of tea. Ignoring the surface: If left undisturbed, the thermal gradient across the teacup wall partly determines the rate of cooling, along with the insulation value of the wall. At maximum differential between tea and air, the tea cools at the fastest rate. After a time, the differential has dropped quite low, the thermal gradient is lower, and the rate of cooling is therefore slower.
One Time Constant is the time it takes to reach 66 2/3 of its final value from whatever value it starts from. Then after the elapse of the 1st TC, in one more TC, it will again reach 66 2/3 of the value it started from at the end of the 1st TC, and so on. After five TCs the system is considered to be at full practical balance in typical systems. More critical systems would alter the point of satisfaction. Mathematically, of course, the system would theoretically never reach complete balance.
Second Order curves are actually several 1st order curves superimposed on each other serially, with the result that the output curve is "S" shaped. It begins movement toward balance rather slowly, is moving at the fastest rate through center, and slows again close to balance.
I suggest referring to a textbook on the topic. The illustrations presented clarify the concept quite considerably.
If we charge several capacitors in parallel through serial resistors, such that each following capacitor charges at a rate determined by the charge level on the previous one, we'll find that the first capacitor charges on a 1st Order curve, and each succeeding one on a 2nd Order curve, with the succeeding curves becoming progressively more "S" shaped. There is a LAG in the transfer from capacitor to capacitor.
The old steam engines did not have the power of modern diesel engines. So what they would do to start the train, is first back up to shorten all the couplings. Then the engine would start forward, taking the slack out of the first, then the second, etc. By this, the engiine would have to start only one car moving at a time. But the last car would be abruptly yanked up to the current speed of the engine. When powerful diesels came into use, it was not uncommon for an engineer from the age of steam to break a train in two like this.
It is the curve shape that is important in visualizing the system dynamics. If you think I'm dodging the question by not supplying explicit examples and problems for you to do for homework, then I guess you'll just have to be unhappy. Take a glass of warm milk before you go to bed.
An electron orbit-decay event displaces the Aether-Line-Of-Force (ALOF) next to it, in the manner of any mechanism generating a compression wave, such as a sound speaker, a baby crying for its mother, or someone demanding math, when he has seen repeated failures of math models.
The 1st ALOF displaces the next, and so on. The result is that by the time the light wavetrain from this particular event reaches from a distant quasar to Earth, the curve is an "S" shape. And the question is: where on that S is the point at which the light is reaching us? that is; what is the redshifting rate as indicated by the slope?
Surely you don't think I can answer that.
What do you think Einstein started out with, a formula with a bunch of unknowns? Are you suggesting he did not plug in empirically-derived values. If you are, then I'm finished talking with you. You contribute absolutely nothing while gleaning as much as you can.
You're a physics leech, a parasite. This is no longer a legitimate discussion, and I certainly have nothing to prove to you. I couldn't care less if you can't get the cobwebs out of your head enough to understand it. Just remember, your posts and mine are all dated and archived.
But thanks for the exercise.
Understand this, if you can: There is no such thing as an "anomaly" or "paradox". There is only ignorance of the contributing factors.
Further, my theory is not complete in all the details, and I have never claimed it so. I call it a General Theory. I do not have the resources to fill it out, but there is no contradiction, anomaly, paradox or "special" part in any of it.
Anomaly: (for instance) the angle measuring apparent irregularities in the movement of a planet.
Paradox: (for instance) a statement self-contradictory, false or absurd.
Einstein was a physicist / mathematician who had a whole lot of help from other people. I do not.
But I'll tell you what I will do. I have seen enough of Einstein's work, and the derivation of his stuff that I'm really sick of it. Anything legitimate he had, he got from others, like Galileo and Newton. When I've finished my book, I will go after Einstein. I won't have much to do, simply because he has already been thoroughly attacked and exposed.
You might try: Ludwik Kostro at: http://itis.volta.alessandria.it/episteme/ep3-24.htm. |
