Point-Mass at it's Orbit: Newton's Equations searched

Forum|Forum|8 years ago
July 5, 2017
3 replies
4297 views

Hello!

I have calculated the complete dynamics for a mass-point moving along a parabola curvation without any resistance like air-resistance, friction, etc.

05-07-2017 21-34-02.jpg

The solution is correctly solved with the Lagrangesche-methos, the movement happens in that way i suggested.

But sometimes it's very complex to create ODEs in that way and therefore it's better to use Newton's Laws.

I tryed to solve the problem with the dynamic balance of forces acting on the mass, but i couldn’t get the same solution in that way so i’m asking what’s wrong. (please see attachement including MP4 and Pdf-file)

Can somebody tell me what’s wrong there?

Thank you very much.

1_Dokuments.zip

Other

F

Fred_Kohlhepp

23-Emerald I

The attached file may help

1_parabola-surface-motion.zip

V

vlehner

Author

1-Visitor

Hi Fred,

In principal i understand what you calculated.

But what i do not understand is: The sign of the force Fhx.

Initial situation:

The body is on the right side and we release it at xo, then it moves along downwards the curvature to the left.

I calculated Fhx as negative and added Ftx, this should be zero.(see sketch)

Fhx (yellow) is acting from right to the left side and will accelerate the body, the force Ftx acts from left to the right because the body has the intension to stay at the position he is (=Trägheitskraft).

If i built the sum, then i have: -Fhx+Ftx=0 what gives a wrong graph, but the dynamic statik says: the sum of all forces have to be zero. In many textbooks i saw this same procedure.

When changing the sign of Fhx to positive, i get a correct graph like you have.

Now i'm confused because i know that the sum of all acting forces have to be zero taking into account their direction they act.

I had the same problem in the thread: https://community.ptc.com/t5/PTC-Mathcad-Questions/Hello-World-See-my-1-st-Prime-Animation/td-p/196317/page/7

neither something in my interpretation is basically wrong, nor something other don't work correctly.

Please explain me.

Thanks for your help.