hi, if i have mass possess potential U(x)=-Gm1m2/(x^2+y^2+(kz)^2 )^1/2 , i said angular momentum of z is conserved but not angular momentum of x , y .. is it correct ? what else is conserved ? energy ?
Yes, the z component of angular momentum is conserved, but the other two are not unless k = 1. As for other conserved quantities, what do you think? You have a potential ...
Are you familliar with Lagrangian mechanics? If so you can use Noether's Theorem to calculate conserved quantities: http://www.mathpages.com/home/kmath564/kmath564.htm It may very well be quicker to just use your physical intuition though.
My thought : angular momentum of z component and the energy of the system is conserved ... Pls tell me if there are more quantities are conserved thanks