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Howdy folks, I'm trying to solve a physics problem that I posed to myself one day after a class. My inspiration is a linear particle accelerator.
So, what I want to do is model a particle in one dimension, being attracted by an inversesquarelaw force.
Object 'M' is the attracting point source, such as a magnet. Object is fixed.
Object 'O' is the object being attracted, obviously free to move.
Distance 'd' is the position of M.
Distance 'x' is the posiition of the projectile.
So, let us assume that the force on 'O' is:
Value S is a unitless abstraction of field strength.
The problem is thus: Find a closedform solution for the position of the object at time 't'.
Any help would be appreciated. I'd prefer someone to just point me in the right direction, and not solve the whole thing for me, but I'll take whatever help I can get.
So, what I want to do is model a particle in one dimension, being attracted by an inversesquarelaw force.
Code:
<d>
<x> 
  
OM
 ^ ^
 
Projectile 

Attracting point source
Object 'O' is the object being attracted, obviously free to move.
Distance 'd' is the position of M.
Distance 'x' is the posiition of the projectile.
So, let us assume that the force on 'O' is:
Code:
S
F = 
(dx)^2
The problem is thus: Find a closedform solution for the position of the object at time 't'.
Any help would be appreciated. I'd prefer someone to just point me in the right direction, and not solve the whole thing for me, but I'll take whatever help I can get.
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