Re: central forces

Oops it was the last part of a question I was attempting and I forgot to include the initial conditions that were given at the start.

>> What's 2e{r} and 3e{theta} ?

I don't post on this forum often so my script may not be what is the norm around here. I mean here e subscript r.
** To make it easier I'm going to let theta = z

{i,j,k} righthanded othonormal basis
x(t) = r(t)[cosz(t)i + sinz(t)j]
v = Re{r} + rZe{z}
r(t)^2Z(t) =h
u(z(t)) = 1/r(t)

I've proved that
d^2u/dz^2 + u = -F(u^-1)/mh^2u^2

So any help with the following is much appreciated

F(r) = -m(36/r^2 + 27/r^3)
and its initial position and velocity is given by
z(0) = 0
x(0) = 2e{r}
v(0) = 3e{z}

Show that,
u(z) = 1/4[1 + cos(z/2)]

Thanks again and happy xmas
.

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