Elliptic path, normal and tangential acceleration

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SUMMARY

The discussion focuses on calculating the speed, 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). Participants identified errors in the initial calculations, particularly in the velocity magnitude and the derivation of the tangential and normal acceleration components. The correct expressions involve using the relationships between velocity and acceleration vectors, specifically the formulas for tangential acceleration (a_T) and normal acceleration (a_N) derived from vector operations. The final consensus emphasizes the importance of correctly applying vector calculus to obtain accurate results.

PREREQUISITES
  • Understanding of vector calculus and derivatives
  • Familiarity with elliptical motion and parametric equations
  • Knowledge of normal and tangential acceleration concepts
  • Proficiency in using trigonometric identities in physics
NEXT STEPS
  • Study the derivation of normal and tangential acceleration in elliptical motion
  • Learn about vector calculus applications in physics, particularly in motion analysis
  • Explore the use of parametric equations in describing motion
  • Investigate the relationship between centripetal acceleration and normal acceleration
USEFUL FOR

Students and educators in physics, particularly those focusing on mechanics and motion analysis, as well as anyone interested in the mathematical modeling of physical systems involving elliptical paths.

  • #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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