Collision 2D

Bluzkin

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Reply #60 on: November 19, 2010, 02:08:33 am »

Hello Fu-Kwun Hwang. This really helped me. For my finals I chose to make a physics simulation application (in Game Maker 8.0) including brownian motion.

I have tried to get the final formula for v₁' with the first two equations but I just can't get it right. Could you maybe send me the the steps you took to get there? That would be great.

I also don't know how to calculate the component of a force (or other vector) in a certain direction so if you could help me with that I would really appreciate it.

Thanks in advance.

(I don't know if I double posted but I think my first post wasn't processed or something...)


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Fu-Kwun Hwang

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Reply #61 on: November 19, 2010, 11:53:24 am »

I assume you know how to find vector which connect between center of two particles.
if one is (x1,y1,z1),another one is (x2,y2,z1). then the vector $\vec{r}$ is (x2-x1,y2-y1,z2-z1).
Assume velocity of particle 1 is $vec{v}$ = (vx1,vy1,vz1),
The velocity component in the vector $vec{r}$ direction can be calculated as $\vec{v_p}=(\vec{v}\cdot\vec{r})/r^2 \vec{r}$ ,where $r$ is the length of velocity $\vec{r}=\sqrt{(x2-x1)^2+(y2-y1)^2+(z2-z1)^2}$

i.e.
vx1'=((vx1*(x2-x1)+vy1*(y2-y1)+vz1*(z2-z1))/r^2) (x2-x1)
vy1'=((vx1*(x2-x1)+vy1*(y2-y1)+vz1*(z2-z1))/r^2) (y2-y1)
vz1'=((vx1*(x2-x1)+vy1*(y2-y1)+vz1*(z2-z1))/r^2) (z2-z1)

And the velocity compendicular to $vec{r}$ is $\vec{v_n}=\vec{v}-\vec{v_p}$

P.S. The inner product between $\vec{A}$ and unit vector $\hat{n}$ will give you magnitude of projection of vector $\vec{A}$ in the direction of $\hat{n}=\vec{r}/r$ , so the component in the direction $\hat{n}$ is $(\vec{A}\cdot\hat{n}) \hat{n}$


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Bluzkin

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Reply #62 on: November 21, 2010, 12:40:39 am »

Thanks! that really helped.

Now I just need to understand JS and have a look at the source code Wink


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lookang

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Reply #63 on: April 11, 2011, 07:51:27 am »

some more error when clicking 'VIEW ejs xml source'
OOPS! EJS XML file (airplane.xml) does not exists!

download it working correctly though Cheesy


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Fu-Kwun Hwang

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Reply #64 on: April 11, 2011, 05:51:32 pm »

Thank you for reporting the problem. It is fixed now.


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