Physics of 2d object collisions using f=ma???

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ralphy (Posted 2004) [#1]

Hi, I need help. Does anyone know of any articles that describe how to calculate the velocities of 2 collided bodies taking account of their objects mass, etc? I.e. similar to colliding asteroids in space. Cheers, Ralphy.

Rob Farley (Posted 2004) [#2]

http://can-do.com/uci/ssi2001/newtonsphysicsnb.html http://www.myphysicslab.com/

ralphy (Posted 2004) [#3]

Thanks Rob. I think the bumper car section has all the info I need.

eBusiness (Posted 2004) [#4]

Just a guess: if a collide with b then: vb=vb+( (va-vb) on (a to b) )*2*(mass a)/( (mass a)+(mass b) ) va=va+( (vb-va) on (b to a) )*2*(mass b)/( (mass b)+(mass a) ) va and vb is the movement vectors. I hope you know vector math Anyway, just a wild guess ;) Edit: Oh by the way, while I keep guessing, I guess this, if true, should only apply to completely hard balls, or circles in 2D.

_PJ_ (Posted 2004) [#5]

Velocities is usually best calculated with momentum and kinetic energy equations... mv = momentum (m(v^2))/2 = K.E. In a system, the total energy will be preserved. KE1a + KE1b = ( KE2a + KE2b )

SwedishChef (Posted 2004) [#6]

Malice... not really... If the collision is elastic, both momentum and KE is conserved. If the collision is inelastic, momentum is conserved whilst KE is not. In other words, momentum is always conserved, KE is sometimes conserved. I assume though that in a game-world you'll have all collisions be elastic. Therefore it'll be easy to calculate the resultant velocities as both KE and momentum is conserved.

ralphy (Posted 2004) [#7]

Using the conservation of momentum equation worked great (thanks Rob for the myphysicslab link). If anyone is interested, this is the code I ended up with and it works perfectt: (debris is object1, others is object2) vcmy = ( (debris\mass*debris\vy) + (others\mass*others\vy) ) / (debris\mass+others\mass) debris\vy = -(debris\vy - vcmy) + vcmy debris\vx = -(debris\vx - vcmx) + vcmx vcmx = ( (debris\mass*debris\vx) + (others\mass*others\vx) ) / (debris\mass+others\mass) others\vx = -(others\vx - vcmx) + vcmx others\vy = -(others\vy - vcmy) + vcmy

StOrM3 (Posted 2004) [#8]

Whoa, you guys rock, I know nothing about physics.. pretty sad actually since 99% of games you create need physics. Although I am thoroughly impressed with the brain power on this forum. Kudos! Ken

Michael Reitzenstein (Posted 2004) [#9]

Using kinetic energy doesn't work - you have the *magnitude* of their velocities, but not their velocities themselves!

Stevie G (Posted 2004) [#10]

Ralphy, debris\vx = -(debris\vx - vcmy) + vcmy is just the same as debris\vx = -debris\vx Obviously, I haven't seen all your code here but all you seem to be acheiving is making the debris and the object bounce off each other with the reverse of their current velocity. The Mass of the debris or other should make no difference? If it seems to work for you .....

Michael Reitzenstein (Posted 2004) [#11]

Stevie, actually it's the same as 2 * vcmy - debris\vx

eBusiness (Posted 2004) [#12]

ralphy, your method doesn't seem to be totally correct, here is an example where it is quite obvious that something is wrong:SeedRnd(1) Graphics 1024,768 Const method=2 Const gravon=0 SetBuffer BackBuffer() Const ballno=1;99 ;Const gravg#=0.0001 Dim x#(ballno) Dim y#(ballno) Dim dx#(ballno) Dim dy#(ballno) Dim mass#(ballno) Dim radius#(ballno) For a=0 To ballno x(a)=Rand(512-50-50+25,512+50+50-25) y(a)=Rand(384-50-50+25,384+50+50-25)+250 dx(a)=Rnd(-1,1) dy(a)=0;Rnd(-1,1) mass(a)=1 radius(a)=20;mass(a)^(1/2.0)*1 Next mass(0)=1 x(0)=200 dx(0)=.5 y(0)=339 x(1)=600 dx(1)=-.5 y(1)=300 mass(1)=1 While Not KeyHit(1) For c=0 To 3 For a=0 To ballno x(a)=x(a)+dx(a) y(a)=y(a)+dy(a);+.0005 dy(a)=dy(a);+.001 If x(a)<10 And dx(a)<0 Then dx(a)=-dx(a) ; If y(a)<10 And dy(a)<0 Then dy(a)=-dy(a) If x(a)>1013 And dx(a)>0 Then dx(a)=-dx(a) If y(a)>757-50 And dy(a)>0 Then dy(a)=-dy(a) Next For a=0 To ballno-1 For b=a+1 To ballno dist#=(x(a)-x(b))^2+(y(a)-y(b))^2 sqrdist#=Sqr(dist)*1000 If gravon=1 Then dx(a)=dx(a)+(x(b)-x(a))*mass(b)/dist/sqrdist dy(a)=dy(a)+(y(b)-y(a))*mass(b)/dist/sqrdist dx(b)=dx(b)+(x(a)-x(b))*mass(a)/dist/sqrdist dy(b)=dy(b)+(y(a)-y(b))*mass(a)/dist/sqrdist End If distmin=(radius(a)+radius(b))^2 If dist<distmin Then If (x(a)+dx(a)-x(b)-dx(b))^2+(y(a)+dy(a)-y(b)-dy(b))^2<dist Then If method=1 Then atobx#=x(b)-x(a) atoby#=y(b)-y(a) lenatob2#=atobx^2+atoby^2 damdbx#=dx(a)-dx(b) damdby#=dy(a)-dy(b) factora#=-(damdbx*atobx+damdby*atoby)/lenatob2 factorb#=(damdbx*atobx+damdby*atoby)/lenatob2 aonatobx#=atobx*factora aonatoby#=atoby*factora bonatobx#=atobx*factorb bonatoby#=atoby*factorb dx(a)=dx(a)+aonatobx*mass(b)/(mass(a)+mass(b))*2 dy(a)=dy(a)+aonatoby*mass(b)/(mass(a)+mass(b))*2 dx(b)=dx(b)+bonatobx*mass(a)/(mass(a)+mass(b))*2 dy(b)=dy(b)+bonatoby*mass(a)/(mass(a)+mass(b))*2 Else vcmy# = ( (mass(a)*dy(a)) + (mass(b)*dy(b)) ) / (mass(a)+mass(b)) vcmx# = ( (mass(a)*dx(a)) + (mass(b)*dx(b)) ) / (mass(a)+mass(b)) dy(a) = -(dy(a)) + vcmy + vcmy dx(a) = -(dx(a)) + vcmx + vcmx dx(b) = -(dx(b)) + vcmx + vcmx dy(b) = -(dy(b)) + vcmy + vcmy End If ; While (x(a)+dx(a)-x(b)-dx(b))^2+(y(a)+dy(a)-y(b)-dy(b))^2<dist ; x(a)=x(a)+dx(a)/2 ; y(a)=y(a)+dy(a)/2+.0025 ; dy(a)=dy(a)+.005 ; x(b)=x(b)+dx(b)/2 ; y(b)=y(b)+dy(b)/2+.0025 ; dy(b)=dy(b)+.005 ; Wend End If End If If gravon=1 Then dx(a)=dx(a)+(x(b)-x(a))*mass(b)/dist/sqrdist dy(a)=dy(a)+(y(b)-y(a))*mass(b)/dist/sqrdist dx(b)=dx(b)+(x(a)-x(b))*mass(a)/dist/sqrdist dy(b)=dy(b)+(y(a)-y(b))*mass(a)/dist/sqrdist End If Next Next Next Cls For a=0 To ballno Oval x(a)-radius(a),y(a)-radius(a),radius(a)*2,radius(a)*2 Next Flip Wend