Interaction between two material points

[kreeb]

Hi,
there are two material points with unitary mass that can move on a stright line. They are subject to a potential of mutual interaction V which depends on x and y and it's not symmetric, where x and y are the coordinates of the two points.
I can choose in the istant 0 v1,v2,x and y. How can I find, in t=0, the force that x and y suffer because of the potential?

 

[ENgez]

I may have misunderstood the question, but if you have the potential field at every point, the force felt should be:

$F=-∇U(x,y)$.

F is the negative of the gradient of U

to simplify even further, if you say the masses move on straight lies only, this becomes a one dimensional problem, as you can express y as a function of x.

 

[kreeb]

Yes, but x e y are coordinates along the same straight line.
I might get the two forces by the derivative of the potential respect to x and y with changed sign, but if you look at how the system evolves at regular intervals, the mechanical energy is not conserved.

 

[kreeb]

up..