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I bring the curve of the second order (hyperbola - red curve) to the canonical form. Why don't my starting blue points end up on a hyperbola transformed to a canonical form. Help me please!
Mathcad 15 in attach.
Solved! Go to Solution.
Instead of changing the value of the angle or using (pi/2-phi) instead of phi you may also just exchange sin and cos in your two rotation equations.
I also wondered why you used the "root" function to calculate phi instead of a direct calculation
This time the sheet is attached 😉
1) You used X instead of X1 in yor second plot
2) The center of the original hyperbola is not in the origin, so you have to translate X and Y by x.o and y0 before you rotate them
3) You angle phi is wrong. Here you see the original hyperbola (matrix H) translated by (x.0; y.0) and rotated by your angle phi
The correct angle to rotate is not 42.659° but rather 90° - 42.659° = 47.341°.
Using all these corrections we get
Thanks, Werner!
Send please the sheet!
@ValeryOchkov wrote:
Thanks, Werner!
Send please the sheet!
Sorry, I did not save and keep the modified sheet.
But only very few changes are necessary and they can easily be taken from the pictures, I think.
That is all that is necessary.
Instead of changing the value of the angle or using (pi/2-phi) instead of phi you may also just exchange sin and cos in your two rotation equations.
I also wondered why you used the "root" function to calculate phi instead of a direct calculation
This time the sheet is attached 😉
Some additional remarks:
You could get the coefficients for your implicit equation more efficient by using the symbolic "coeff" command so you can avoid copy&paste:
And while I think that implicitplot2D() is a most valuable tool, you don't need it to plot hyperbolas as you could use a parameter equation
Dummy is x^3.
@ValeryOchkov wrote:
Dummy is x^3.
No, "dummy" is the coefficient of x^5 which would correspond to (non-existent) x^2*y in the original expression.
Yes! With dynamic: sh(t), ch(t)...
Origin seven (five) points (the Asteroid position in time), our blue planet, two branches of hyperbola, two focus, two asymptotes, two directrices and... new method of hyperbola transforming to a canonical form. Or it is one old method?
Sorry, I don't understand your question.
Is it one new method of transforming one curve of 2-d order in canonical form. With using one Math package?
I guess its not really new but rather a bit different from the usual way of using matrices, eigenvalues, etc. But the basic math is quite similar, I suppose.
Many students are horrified by words eigenvalues, etc. And so - "not aesthetically pleasing, but cheap, reliable and practical" using the numerical solution of systems of equations.
SMath
(67) Лёлик, но это же не эстетично! Зато дёшего, надёжно и практично! - YouTube
@ValeryOchkov wrote:
Many students are horrified by words eigenvalues, etc. And so - "not aesthetically pleasing, but cheap, reliable and practical" using the numerical solution of systems of equations.
In other words .. KISS 😄