Finding x and y co'ordinates at a given time?

Questions
,
1

Apologies if this question has been asked elsewhere / is a stupid question.
I’m fairly new to Mathematica syntax and doing a Mathematica-heavy project so any help will be much appreciated.

Basically I’m doing a simulation of scattering of particles. I have two equations regarding the x and y accelerations,

x''[t] == ( k x[t]/(x[t]^2 + y[t]^2)^(3/2) ), y''[t] == ( k y[t]/(x[t]^2 + y[t]^2)^(3/2) )

Using

path := NDSolve[ {x''[t] == (5.48147 x[t]/(x[t]^2 + y[t]^2)^(3/2)), 
   y''[t] == (5.48147 y[t]/(x[t]^2 + y[t]^2)^(3/2)), 
   x'[0] == 155000000, y'[0] == 0, x[0] == -10*10^-15, 
   y[0] == 5*10^-16}, {x[t], y[t]}, {t, 0, 10^-22}]

and

ParametricPlot[Evaluate[{x[t], y[t]} /. path], {t, 0, 10^-22}, 
 PlotPoints -> 1000]

I’ve managed to plot the correct graph. However, I need to find the x and y co’ordinates for a given value of t. I don’t have any real idea of where to go on this and have been stuck on this for a while, I’d really appreciate it if anyone could help me on this.

2

Hi,

(* this returns x and y at t=1.E-23 *)
Flatten@Evaluate[{x[t], y[t]} /. path] /. t :>  10^(-23) 
(* this creates a table of x and y vals. *)
ListPlot@Table[Flatten@Evaluate[{x[t], y[t]} /. path] /. t :>  i , {i, 0, 10^-22, 1/20 (* <- # of points *) 10^-22 }]

Also, EventLocator method for NDSolve[] might be of interest to you as well as documentation about ref/InterpolatingFunction

I.M.

3

Thank you! This is exactly what I needed. :slight_smile: