[R] Movement within a circle

[Juliane Struve]

Dear list,
 
I am trying to program semi-random movement within a circle, with no particles leaving the circle. I would like them to bounce back when they come to close to the wall, but I don't seem to be able to get this right.  Would somebody be able to give me a hint ? This is my code so far, the particle starts at some point and moves towards the wall, but I don't get the "bouncing off" part right .
 
Any help would be much appreciated.
 
Juliane 
 
days=10
circularspace=data.frame(day=c(0:days),xcoord=1,ycoord=1,xvelocity=1,yvelocity=1,xdistwall=0, ydistwall=0, wallxvel=0, wallyvel=0,stochasticxvel=0,stochasticyvel=0)
xmax=10
xmin=-10
ymax=10
ymin=-10
mindist=8
plot(xmin:xmax, ymin:ymax, type = "n")
circularspace
radius=10
timesteplength=1
weightfactor=1
for(i in 1:days)
{
#This is the stochastic component of the movement
circularspace$stochasticxvel[day=i+1]=runif(1,min=-1,max=1)
circularspace$stochasticyvel[day=i+1]=runif(1,min=-1,max=1)
#This is calculating the movment speed 
circularspace$xvelocity[day=i+1]=weightfactor*(circularspace$xvelocity[day=i])+ (1-weightfactor)*circularspace$stochasticxvel[day=i+1]
circularspace$yvelocity[day=i+1]=weightfactor*(circularspace$yvelocity[day=i])+ (1-weightfactor)*circularspace$stochasticyvel[day=i+1]
#This is calculating the new position
circularspace$xcoord[day=i+1]=circularspace$xcoord[day=i]+circularspace$xvelocity[day=i]/timesteplength
circularspace$ycoord[day=i+1]=circularspace$ycoord[day=i]+circularspace$yvelocity[day=i]/timesteplength
#Tis is checking the distance from the wall
circularspace$xdistwall[day=i+1]=xmax-abs(circularspace$xcoord[day=i])
circularspace$ydistwall[day=i+1]=ymax-abs(circularspace$ycoord[day=i])
#This is updating the movement if distance to wall too small
if (circularspace$xdistwall[day=i+1] <= mindist){
circularspace$wallxvel[day=i+1]= -1*(circularspace$xcoord[day=i+1])
circularspace$xvelocity[day=i+1]=weightfactor*circularspace$xvelocity[day=i]+ (1-weightfactor)*circularspace$stochasticxvel[day=i+1]+ circularspace$wallxvel[day=i+1]
circularspace$xcoord[day=i+1]=circularspace$xcoord[day=i]+circularspace$xvelocity[day=i]/timesteplength
}
if (circularspace$ydistwall[day=i+1] <= mindist){
circularspace$wallyvel[day=i+1]= -1*(circularspace$ycoord[day=i+1])
circularspace$yvelocity[day=i+1]=weightfactor*circularspace$yvelocity[day=i]+ (1-weightfactor)*circularspace$stochasticyvel[day=i+1]+ circularspace$wallyvel[day=i+1]
circularspace$ycoord[day=i+1]=circularspace$ycoord[day=i]+circularspace$yvelocity[day=i]/timesteplength
}
points(circularspace$xcoord[day=i+1],circularspace$ycoord[day=i+1])
symbols(0,0,circles=radius,inches=F,add=T)
symbols(0,0,circles=radius-2,inches=F,add=T)
}
circularspace
 Dr. Juliane Struve
Environmental Scientist
10, Lynwood Crescent
Sunningdale SL5 0BL
01344 620811