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Post by mondo on Sept 10, 2022 17:03:39 GMT
From the plot I can tell the red curve has the oval "tendency" so I decided to manipulate parameters a bit and here is what I got after decreasing $c$ from $2$ to $0.5$:  The key is to manipulate our constant $c$. This shows what can also be seen from the expanded equation I did in previous post - as $c$ tends to $0$ $e^c$ tends to 1 and imaginary part cancels out leaving pure real component. Hence in the limit this oval will turn into horizontal line. Is my understanding correct here? |
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Post by Admin on Sept 10, 2022 17:55:08 GMT
Mondo
Try doing it with different values of $c$. If you think about it as $c$ gets larger the ellipse gets closer to the large circle and the small circle gets smaller and smaller. $c=0$ should give you a straight line. Try $c=0.1, 0.2,...$etc up to 1.
If you look at the diagram in the book you will see that the particle moves along horizontal lines at a distance $c$ and $-c$ from the real axis and the other particles move along the two circles and the ellipse.
By the way that's not a rounding error its because your step for $t$ is too large and so you get a curve with corners on it.
Vasco
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Post by Admin on Sept 10, 2022 18:03:35 GMT
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Post by mondo on Sept 10, 2022 22:23:29 GMT
Mondo Try doing it with different values of $c$. If you think about it as $c$ gets larger the ellipse gets closer to the large circle and the small circle gets smaller and smaller. $c=0$ should give you a straight line. Try $c=0.1, 0.2,...$etc up to 1. If you look at the diagram in the book you will see that the particle moves along horizontal lines at a distance $c$ and $-c$ from the real axis and the other particles move along the two circles and the ellipse. Yes, thank you. I got to this conclusion in my post #15 too. By the way that's not a rounding error its because your step for $t$ is too large and so you get a curve with corners on it. So you suggest there is no enough points? I don't think so. Let's compare 10 points plot when the argument is a fraction of $\pi$:  with a plot when the argument is just an integer multiple:  Hence, we have the same number of steps (10) and the only difference is in one case I pass a fraction of $\pi$ vs integer multiple. This looks to me as $\cos(), \sin()$ rounding problem since the later is not radian "friendly". |
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Post by mondo on Sept 10, 2022 22:49:52 GMT
Wow! This is really nice. Thank you Vasco. |
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