Printable View
I've spent hours trying to figure this out. I'm building a particle engine for my thesis and I am having a hard time with this part of it.
I have two particles colliding and I need to know their resulting trajectories.
I know:
Mass of both particles
Velocities of both particles (both angle, magnitude and in vectors)
I know the angle between them
Attached is a diagram.
The distance between the two and the radii of them need to be irrelevant.
Is this collision perfectly elastic/inelastic?
Don't forget that you can use conservation of momentum to help you solve it.
I hope that helps.
I would help, but your picture is broken.
It's perfectly elastic; ie there is no friction from the particles bouncing off of each other. I'm trying to conserve momentum.Quote:
Originally Posted by R.D.735
Weird, the picture works fine for me. Here's an embedded one:
http://www.dreamviews.com/community/...7&d=1205514503
I just get a red x, can you upload it on imageshack or something? Or maybe just write out the variables.
I mentioned all the variables :P
Here is it on imageshack
http://img139.imageshack.us/img139/5426/39764143va7.jpg
Can't see that eiher, and I meant numbers :P.
No numbers, I need to solve it for a general situation.
Maybe if I don't embed the image: http://img139.imageshack.us/img139/5426/39764143va7.jpg
I'll describe the pictures
I have an angle between the particles (the normal to their touching surfaces), I can use it as either the angle or a normalized vector [dx, dy]
The mass variables are m1 and m2
The velocity is stored in vectors [vx, vy]. Of course I can go to angle and magnitude if I need to with Pythagorean theorem and inverse tangent.
From that information I'm trying to figure out an algorithm to figure out the trajectory of the particles after the collision (preserving momentum) for a perfectly elastic collision and store them in a vector [tx, ty] for both particles.
If I can do it all with vectors I'd be happy, but I doubt it. I can convert to magnitude + angle to [x, y] very easily.
Image cannot be displayed because it contains errors.
Maybe PCs can't do CYM colour, here's an RGB image.
http://img246.imageshack.us/img246/1244/25097167gw1.png
Hey, I can see that :P.
It's a little different than anything I've worked with before, but I'll see if I can think of anything...
http://en.wikipedia.org/wiki/Elastic_collision
complete with animations and everything!
Thanks for that, but Grrrrrr. My algorithm only works in one dimension. Please tell me what I'm doing wrong, I've spent two days on this trivial part of my program.
It's GNU C. The structure of the particles should be obvious:
x, y are position
vx, vy are velocity along the axis
I know it's bad code :P I'm from the school of make it work, then make it fast :)Code://get the normal to the collision
float dx = spheres[p1].x - spheres[p2].x;
float dy = spheres[p1].y - spheres[p2].y;
float theta = atan2(dx, dy);
//get the angle of the Velocities
float vangle1 = atan2(spheres[p1].vx, spheres[p1].vy);
float vangle2 = atan2(spheres[p2].vx, spheres[p2].vy);
//rotate the angles into the normal to collision axis
vangle1 = vangle1 - theta;
vangle2 = vangle2 - theta;
//Pull out the velocities' magnitude
float u1 = Velocity(p1);
float u2 = Velocity(p2);
//change velocity vectors to new coordinate system
spheres[p1].vx = sinf(vangle1) * u1;
spheres[p1].vy = cosf(vangle1) * u1;
spheres[p2].vx = sinf(vangle2) * u2;
spheres[p2].vy = cosf(vangle2) * u2;
//take out mass so the forumula is easier to read
float m1 = spheres[p1].mass;
float m2 = spheres[p2].mass;
//handle velocities for the new x axis
float v1 = (spheres[p1].vx * (m1 - m2) + (2 * m2 * spheres[p2].vx)) / (m1 + m2);
float v2 = (spheres[p2].vx * (m2 - m1) + (2 * m1 * spheres[p1].vx)) / (m1 + m2);
spheres[p1].vx = v1;
spheres[p2].vx = v2;
//handle velocities for the new y axis
v1 = (spheres[p1].vy * (m1 - m2) + (2 * m2 * spheres[p2].vy)) / (m1 + m2);
v2 = (spheres[p2].vy * (m2 - m1) + (2 * m1 * spheres[p1].vy)) / (m1 + m2);
spheres[p1].vy = v1;
spheres[p2].vy = v2;
//get the angle of the new Velocities (still in new coordinate system)
vangle1 = atan2(spheres[p1].vx, spheres[p1].vy);
vangle2 = atan2(spheres[p2].vx, spheres[p2].vy);
//rotate back into x/y coordinate system
vangle1 = vangle1 + theta;
vangle2 = vangle2 + theta;
//Pull out the velocities' magnitude from the collision coordinate system
u1 = Velocity(p1);
u2 = Velocity(p2);
//change velocity vectors back to x/y coordinate system
spheres[p1].vx = sinf(vangle1) * u1;
spheres[p1].vy = cosf(vangle1) * u1;
spheres[p2].vx = sinf(vangle2) * u2;
spheres[p2].vy = cosf(vangle2) * u2;
If I swap v1 and v2 for the second velocity calculation it works alright until I introduce two particles of different mass.
You say it works in one dimension... is it just the X dimension? Does it work in just the Y dimension? Try getting them to work separately. It eliminates a whole lot of unknowns.
It works in any direction, x axis, y axis, arbitrary angle... it just only moves them apart parallel to velocities, if they are offset a little bit they should fly off at an angle to that, but don't.