Is there any meaning to the arc-length of Euclidian Cartesian plots?

[steveupson]

No, you do not want to learn, what you want to do is to continue posting nonsense. If you wanted to learn, you would have started by taking a break from posting and by taking a class in vector calculus.

 

 

 

 

There is no such thing as [latex]c-n_1[/latex]. Light speed doesn't add/subtract.

 

 

 

 

 

There is no such thing as [latex]c-(n_1+n_2)[/latex].Light speed doesn't add/subtract.

 

 

Yes. Like I said before, you're probably right and I'm probably wrong. I guess I'm wrong about wanting to learn, too. You probably know much better about that than I do.

 

In any event, can you plot the velocity of image A vs time and image B vs time? Or even better, can you plot the displacement of image A vs time and image B vs time? Assume that the twin quasar is 7,800,000,000 ly distant from earth.

Since the displacement is the same, and the magnitude of the velocity is the same, by your methods the the two graphs should be identical, shouldn't they?

 

No, what you are missing is a working knowledge of the definition of an ad hominem argument.

 

Rather than respond to the issues that have been raised you choose to offer opinions about me. What would you call it?

[zztop]

 

 

Yes. Like I said before, you're probably right and I'm probably wrong. I guess I'm wrong about wanting to learn, too. You probably know much better about that than I do.

 

You are surely wrong. Why don't you take a break from posting and take a class in vector calculus?

 

 

In any event, can you plot the velocity of image A vs time and image B vs time? Or even better, can you plot the displacement of image A vs time and image B vs time? Assume that the twin quasar is 7,800,000,000 ly distant from earth.

Since the displacement is the same, and the magnitude of the velocity is the same, by your methods the the two graphs should be identical, shouldn't they?

There is no such thing as "velocity of image", there is no answer to the nonsense you post.

[Phi for All]

Rather than respond to the issues that have been raised you choose to offer opinions about me. What would you call it?

 

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Moderator Note

No opinions about you were offered. Critique was given about the science you presented. Please learn to distinguish between an argument aimed at you personally and one aimed at your knowledge or lack thereof.

 

Also, you're dragging this topic away from its intent. If you have specific questions about physics, ask them in a thread of your own making, rather than forcing everyone else to explain tangentially.

[steveupson]

I think my questions have all been answered. Thank everyone for their participation.

[studiot]

 

 

Would it? Take a plot, and plot, and invert it. Same arc length. Vastly different results for the end value.

 

 

The only information I have been able to come up with is this: the minimum length is for a constant function. If the arc length is not the minimum, the function is not a constant.

 

edit: there also may be other min/max or optimal/not optimal situations that could be present.

 

Yes that was an extremely bad example to offer please delete it or add a note to that effect.

 

The rest of my examples are good however.

 

I did however take the OP to be a general question about arc length, and the reference to parabolas, movement or plots just an example.

[steveupson]

 

There is no such thing as "velocity of image", there is no answer to the nonsense you post.

 

 

Of course. This should have read velocity of light observed as image A or B.

[swansont]

Yes that was an extremely bad example to offer please delete it or add a note to that effect.

 

The rest of my examples are good however.

 

I did however take the OP to be a general question about arc length, and the reference to parabolas, movement or plots just an example.

Right. But the arc length doesn't distinguish between e.g. a concave parabola vs a convex parabola.

[studiot]

Right. But the arc length doesn't distinguish between e.g. a concave parabola vs a convex parabola.

 

Agreed but I don't see the relevance of why it should be expected to any more than just the arc length will distinguish between a parabola and another curve which just happens to have the same length.

[swansont]

Agreed but I don't see the relevance of why it should be expected to any more than just the arc length will distinguish between a parabola and another curve which just happens to have the same length.

I don't think anyone has suggested otherwise.

[imatfaal]

Thinking about velocity time plots - and to simplify a set with equal area under the line (distance travelled) and equal change in t (time taken) - does the arc length provide useful information about the amount of acceleration? By useful I mean that the data are summarized in the arc length in a way that is relatively unambiguous (obviously it is blind to concavity/convexity), translatable to the physical quantity, and useful in interpreting the information provided.

 

For example - I have a set of velocity time plots of identical time and distance covered (every day to the office and back home, within 2 percent same time and exact same distance) - those with an abnormally high arc-length will be exactly those with high energy expenditure(I track this too) and I bet with higher than average Heart beats per min

[Bender]

This is all related to some kind of variability. Not necessarily the acceleration itself, but the number of times it changes. In your particular example, it would mainly give a measure of the number of times you stopped and started again. It also only works because it is normalised in the way that the distance is always the same. Things that are correlated with the variability, could also be correlated with the arc length.

edit: of course: you could just do some kind of regression analysis instead.

[imatfaal]

This is all related to some kind of variability. Not necessarily the acceleration itself, but the number of times it changes. In your particular example, it would mainly give a measure of the number of times you stopped and started again. It also only works because it is normalised in the way that the distance is always the same. Things that are correlated with the variability, could also be correlated with the arc length.

edit: of course: you could just do some kind of regression analysis instead.

 

It is necessarily related to the acceleration in a velocity time graph - a constant velocity is a straight horizontal line (min length of curve) constant acceleration through period is a straight line, varying acceleration is a curve; the more time spent accelerating and the more violent that acceleration the higher the arc length. I am sure I could dig out a ride with almost no stops or restarts yet with massive variation in velocity - interval training would be the obvious example (many small periods of rapid acceleration followed by short recovery)

 

And I would not say normalised - it is a relative comparison which could be made absolute.

 

You talk about correlation with the variability - how are you measuring/quantifying the variability? That is the nub - is there a nicer and more obvious measure than the arc length?

 

And I am not talking about statistical correlation - but rather the more concrete connexions; acceleration needs force ->torque -> power

[Bender]

 

It is necessarily related to the acceleration in a velocity time graph - a constant velocity is a straight horizontal line (min length of curve) constant acceleration through period is a straight line, varying acceleration is a curve; the more time spent accelerating and the more violent that acceleration the higher the arc length. I am sure I could dig out a ride with almost no stops or restarts yet with massive variation in velocity - interval training would be the obvious example (many small periods of rapid acceleration followed by short recovery)

 

And I would not say normalised - it is a relative comparison which could be made absolute.

 

You talk about correlation with the variability - how are you measuring/quantifying the variability? That is the nub - is there a nicer and more obvious measure than the arc length?

 

And I am not talking about statistical correlation - but rather the more concrete connexions; acceleration needs force ->torque -> power

Interval training is changing the acceleration often, even if you don't stop completely. The average of the acceleration will have less impact on the arc length then the number of changes and the size of the change.

 

I called it normalised because it only works if you don't vary the time or the distance between runs, which has the same effect as a normalisation.

 

In retrospect, I was thinking about Root-mean-square deviation rather than regression, but neither works well. A frequency analysis might, or perhaps the rms of the jerk.

Edited February 25, 2017 by Bender

[imatfaal]

Interval training is changing the acceleration often, even if you don't stop completely. The average of the acceleration will have less impact on the arc length then the number of changes and the size of the change.

 

The average of the acceleration will be zero - I have no velocity at the beginning or the end. Interval training is change in velocity and it is exactly the number and size of the change of velocity that would be neatly captured

 

 

I called it normalised because it only works if you don't vary the time or the distance between runs, which has the same effect as a normalisation.

 

It is not normalised - one just needs to understand the units. I could tell you that my last ride was at an average power of 24.7 gigaMade-ups and you would know nothing; but if I said it was at 345 Watts then you would know something - moreover if I said that I averaged 345 Watts for 100 yards - meh, over 1 mile it would be unimpressive, but over 60 miles it would be good, over 160 miles bloody amazing.

[swansont]

Arc length won't distinguish between oscillating functions where you e.g. raise the frequency and lower amplitude

[steveupson]

Interval training is changing the acceleration often, even if you don't stop completely. The average of the acceleration will have less impact on the arc length then the number of changes and the size of the change.

 

I called it normalised because it only works if you don't vary the time or the distance between runs, which has the same effect as a normalisation.

 

In retrospect, I was thinking about Root-mean-square deviation rather than regression, but neither works well. A frequency analysis might, or perhaps the rms of the jerk.

 

If the variation is cyclic in nature then wouldn't it be a candidate for Fourier analysis, and if it isn't cyclic then wouldn't it be a candidate for fractal analysis?

[swansont]

If the variation is cyclic in nature then wouldn't it be a candidate for Fourier analysis, and if it isn't cyclic then wouldn't it be a candidate for fractal analysis?

What does that have to do with the OP?

[steveupson]

What does that have to do with the OP?

Try and keep up. The OP asked about the significance of the arc length in a velocity vs time or displacement vs time graph. At least two of our members (and perhaps yourself) are discussing how the arc length would be determined. I asked them a question because they seem to know stuff.

 

Of course to me, the better - more interesting - question is what do you have when you know the arc length. That’s what I interpret the OP to be asking. I’ve also been informed by the moderation staff (right on que) that my views are not to be considered for discussion.

 

Maybe it’s because ya’ll can’t keep up. That seems to be your problem.

 

I would suggest that when you do figure out what you’re doing and what you’re talking about that you consider what dimension the arc length is in. But oh wait, we can’t go there, can we? Even when another member asks this identical question.

 

[swansont]

Try and keep up. The OP asked about the significance of the arc length in a velocity vs time or displacement vs time graph. At least two of our members (and perhaps yourself) are discussing how the arc length would be determined. I asked them a question because they seem to know stuff. [/size]

Of course to me, the better - more interesting - question is what do you have when you know the arc length. That’s what I interpret the OP to be asking. I’ve also been informed by the moderation staff (right on que) that my views are not to be considered for discussion. [/size]

Maybe it’s because ya’ll can’t keep up. That seems to be your problem.[/size]

I would suggest that when you do figure out what you’re doing and what you’re talking about that you consider what dimension the arc length is in. But oh wait, we can’t go there, can we? Even when another member asks this identical question.[/size]

OK. Explain to me how Fourier analysis determines the arc length.

[Bender]

A lot of energy in higher frequencies would be correlated with a large arc length.

[studiot]

Returning to the OP topic;

 

Here is a good presentation of he calculation of area of revolution, incorporatingand extending the idea of arc length.

 

you can tab back to their presentation of arc length

 

http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx

[Bender]

Of course you can have a parabola of velocity vs time. Nobody is talking about infinite graphs here, otherwise it would make no sense to calculate the arc length, which would also be infinite, regardless of anything else.

[studiot]

This recent thread in homework shows an interesting use of arclength.

 

http://www.scienceforums.net/topic/103512-force-and-laws-of-motion/

 

Please also note that just because the plot region extends to infinity, it does not mean that the arc length of the plotted curve is infinite.

 

For example the plotted arclength of

 

x² + y² = 1

 

is finite whatever the size of the plot area.

Edited March 3, 2017 by studiot

[swansont]

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Moderator Note

FYI, posts have been split off to the trash (IOW Bender's recent response is not the non-sequitur it might appear to be)