I am actually doing monte Carlo simulations, bravo.
I guess defining it is my issue. I'm not sure how one can define/examine what role the set of A's had in whatever the final answer is for X.
The variables are independent.
I was thinking of doing something similar to what you suggest in...
Say that there is an object
X = <ABC> = (A_1B_1C_1+A_2B_2C_2+...+A_NB_NC_N)/N
Is there any way to say what X_A is? Or what exactly the A term in all of these terms contributed to X? Or is that info pretty much washed out in this type of ensemble average?
Oh, and A, B and C are random...
If the impulse was purely radial the angular momentum wouldn't change right? Shoot, have I done something wrong with the original problem since the angular momentum would change? I plugged it into the integral and treated as a constant. I'm not sure if there is a mistake there or not now...
So, TSny and Haruspex I think I've got this one figured out. What if the radial velocity at time = 0 isn't 0? What if the particle is given some type of kick outward or inward? Would I then want to turn it into a 2nd order D.E. so I could take that initial condition into account? Or is there a...
The equation it gives me is the one just above your post I believe.
I suppose you're right I maybe should not take the time derivative. I guess E can be found with the initial conditions. E = \frac{L^2}{2mr_o^2}-\frac{k}{2r_o^2}
from there I have a first-order equation I suppose.
Oops yes, that is the 2nd time derivative of r(t)
E = \frac{1}{2}m(\frac{dr}{dt})^2+\frac{L^2}{2mr^2}-\frac{k}{2r^2}
take the time derivative of this equation and that is how I got the expression from my previous post. L is the angular momentum, yes.
Homework Statement
I'm given a force law is F = \frac{-k}{r^3} and that initially, the particle is in a circular orbit the particle is given an impulse parallel and in the opposite direction to its velocity find the distance from the center for the particle as a function of time.
Homework...