Elliptic path, normal and tangential acceleration

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The discussion focuses on calculating the speed and the normal and tangential components of acceleration for a point mass moving in an elliptical path defined by the equations x = a cos(ωt) and y = b sin(ωt). The initial calculations for velocity and acceleration components contained errors, particularly in the magnitude of velocity and the signs in the equations. Participants suggest using vector operations to derive the components of acceleration more effectively, emphasizing the importance of separating the components from the unit vectors. The conversation highlights the need for careful application of vector calculus to achieve correct results, particularly in the context of special relativity. Overall, the thread illustrates the complexities involved in analyzing motion in a non-linear path.
  • #31
@ehild Still no canceling out... I really don't see it. :/ (I wrote only the top line in the attached file because it's so long)
 

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  • #32
JulienB said:
@ehild Still no canceling out... I really don't see it. :/ (I wrote only the top line in the attached file because it's so long)
You forgot to square sin and cos in v^2
 
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  • #33
@JulienB
##(\vec v)^2=w^2(a^2\sin^2(wt)+b^2\cos^2(wt))##
##(\vec a)^2=w^4(a^2\cos^2(wt)+b^2\sin^2(wt))##
What is their product?
 
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  • #34
@ehild aaaah it worked out now! I get the same result as with the other method! Thanks a lot, that was crazy! ;)

Julien.
 
  • #35
JulienB said:
@ehild aaaah it worked out now! I get the same result as with the other method! Thanks a lot, that was crazy! ;)

Julien.
Well done. I must sleep now but tomorrow I show you how the formula you used is connected to vector products.
 
  • #36
@ehild Thanks a lot! I must sleep too otherwise I would post the correct calculation again. I'll do it tomorrow.
 

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