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24-Ruby IV
November 29, 2022
Question

A curve, or not a curve, that is the question?

  • November 29, 2022
  • 1 reply
  • 2676 views

Here a dispute arose.
1. Is this closed curve (a phase portrait) an ellipse? The ellipse has two foci. How to calculate the abscissa of the focus of this "ellipse"?

2. Can this object be called a curve? The curve has a length. How to calculate the length of this curve?

PhPorPend.png

1 reply

25-Diamond I
November 29, 2022

Of  course is what you define a parameter representation of an ellipse but "t" must run up to approx. 2.00641 s with an appropriate step size to make it really a "closed" one.

 

But how can you expect this curve having a LENGTH? You are operating in a plane where the horizontal direction is of dimension time^-1 while the vertical direction is dimensionless. How wold you define LENGTH or DIRECTION in this context?

To make it work you either have to make all dimensionless or make equal dimensions in any direction (preferably dimension length, otherwise talking about the "length" of the curve would not make much sense 😉
To make the point more clear: In the following plot we can say that the slope is  0,75 kV/ms, but what would you say is the "length" of that straight line segment? Which unit would you apply???

It seems to make no sense to ask for a "length" in this setting with units.

Werner_E_0-1669765627646.png

 

 

P.S.: You did not attach the worksheet and I am too lazy to retype - whats the error message. My translation tells me that it means something like "Are you a total fool?" but this would not be very polite for an official error message.

24-Ruby IV
November 30, 2022

Thanks Werner for your reply.
But the questions were.
If it's not an ellipse, then what is it?
If that's not a curve, then what is?

19-Tanzanite
November 30, 2022

Does this answer your question Val?

g0.png

Alan