How do I turn this function into a 2-D operation?

I have this function file:

if true
  %     function [newx,newv,F]=Leaf(x,v,m,h)
  %   Inputs are x (meters), 
  %              v (meters/second), 
  %              m (kg)
  %   Outputs are newx (meters)
  %               newv (meters/second), 
  %               F (Newtons)
  % Equations
  F = 0.2.*sin(x).*(x.^2+x); 
  a = F./m; 
  newx = x+h.*v; 
  newv = v+h.*a; 

    end
  end

I need to know make it into a two dimensional operator with the functions:

*        r(x,y) = sqrt((x.^2)+(y.^2));
*    theta(x,y) =  atan(y./x);
*       Fx(x,y) = -0.01 sin(theta(x,y))-0.01.*r(x,y).*x
*       Fy(x,y) = -0.01 cos(theta(x,y))-0.01.*r(x,y).*y
*   x(n+1) = x(n) + h*v
*   v(n+1) = v(n) + h*a
*        a = F/m

I am not really sure how 2-D vectors set up in these functions. Thank you

Answer 1

[Star Strider]

You can make any of them into anonymous functions. For instance:

Fx = @(x,y) -0.01 sin(atan2(y,x))-0.01.*hypot(x,y).*x;

I did some substitutions to take advantage of built-in functions that would at least be a bit more efficient and faster, and probably more precise.