NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/
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 Author Topic: Collision 2D  (Read 154071 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
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 « Embed this message on: November 19, 2004, 09:09:24 am »

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The following is a simulation for elastic collision which means that
1. the momentum is conserved: $m_1\vec{V_1}+m_2\vec{V_2}=m_1\vec{V'_1}+m_2 \vec{V'_2}$ where $m_1,m_2$ are mass for each object, $\vec{V_1},\vec{V_2}$ are velocity vectors before collision,$\vec{V'_1},\vec{V'_2}$ are velocity vectors after collision.
2. the total energy is conserved: $\frac{1}{2}m_1\vec{V_1}^2+\frac{1}{2}m_2\vec{V_2}^2=\frac{1}{2}m_1\vec{V'_1}^2+\frac{1}{2}m_2\vec{V'_2}^2$
For collision in 2D, there are four unknow, however, there are only three equations. Because the contact point is missing in the above equations.
To solve the above problem, we can break 2D collision problem into two 1D collision problem once we know the contact point (when collision happened).
We use x-y coordinate to describe the position of those two balls before and after the collision.
At the time when two balls just in contact with each other, we can choose a new coordinate system:
1. direction from center of mass of $m_1$ to center of mass of $m_2$: The interaction forces bwteen those two balls during collision is limited to this direction. It become a 1D collision problem in this direction.
2. direction which is perpendicular to the above direction: Assume there is no friction between those two balls, no rotation effect to be considered, then the velocity component for those two balls in this direction will not be changed when collision happened (Because the interaction force dose not have component in this direction).

This simulation shows the physics of two ball collide in 2D (without any rotation motion).
What can be changed:
• The sliders on either side change the vertical position of each ball

• mass(m) and initial horizontal velocity(vx) can be adjusted with slider bar

• Use mouse click and drag to change the position (click near the center of the ball) or the velocity vector (click near the arrow)

• check out the "paused when collide" checkbox to show more detail process during collision,
Click mouse in the area to play it again

Physics processes:
1. when two ball meets, the program shows two components of the velocity for each ball (along the line connect two ball and perpendicular to it)

2. Interaction (force) between balls is along the line connect two balls

3. Velocitys perpendicular to connection line are not changed (No force/interaction in that direction)

4. The rest of the problem is similar to 1D collision problem for ball with velocity along the line

5. Because this is a 2D simulation, so the radius is proportional to the square root of the mass to keep the same density (for those balls).

You need to understand conservation of momentum and conservation of energy.
The velocity of two objecs after collision (V1',V2')can be calculated from velocity before collisions (V1,V2) and mass of two objects (m1,m2).

V1'= (m1-m2)*V1/(m1+m2) + 2*m2*V2/(m1+m2)= (m1V1+m2V2)/(m1+m2)+(V2-V1)*m2/(m1+m2)=Vcm+(V2-V1)*m2/(m1+m2);

V2'=2*m1*V1/(m1+m2)+(m2-m1)*V2/(m1+m2)=(m1V1+m2V2)/(m1+m2)+(V1-V2)*m1/(m1+m2)=Vcm+(V1-V2)*m1/(m1+m2);

Where Vcm=(m1V1+m2V2)/(m1+m2);
Before the collision, the velocity of m1 relative to Vcm is
V1-Vcm=V1-(m1V1+m2V2)/(m1+m2)=m2(V1-V2)/(m1+m2)
compare it with the second term in V1'

If m1=m2 then V1'=V2, V2'-V1 ;
it means that both particles just exchange velocity.
If m1>> m2 then V1' ≒ V1 ; V2'≒ 2V1+V2;
i.e. If a heavy car hit you with velocity V1=50km/hr , you will fly out with velocity 2V1=100km/hr.
If m1<< m2 then V1' ≒ -V1+2V2 ; V2'≒ V2;
i.e. If a small ball hit a wall (V2=0),then the ball will be bounced back (same magnitude,oppositive direction).

For collision 2D, the trick is to transform it into collision 1D problem:
In the direction of red arows, and another direction normal to red arrows (i.e. direction of green arrows).
If friction is not considered (which will cause both balls to rotate due to friction force),
Then green arrow velocity is not changed after the collision because there is no force in that direction.
And collision in red arrow direction is 1D collision problem, so you can use the above equation.
However, you need to calculate the component of velocity in red arrow direction. (This you need to understand the meaning of inner product -- mathematic operation).

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 « Embed this message Reply #1 on: August 13, 2007, 04:34:03 pm » posted from:Pune,Maharashtra,India

Hello Professor,

I am trying to develop a simple table/board game and was looking for some "good" physics to apply to the game - like -angle, velocity, friction, collision etc.

I got a fair idea from your other articles, but this one is close enough to what i was looking for.

Is it possible for you to share the source code for this one so that I can extract the required algoriths from it?

Thanks.
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Fu-Kwun Hwang
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 « Embed this message Reply #2 on: August 13, 2007, 06:09:04 pm »

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-*-

Here is a modified version of the above simualtion:

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 « Embed this message Reply #3 on: August 14, 2007, 11:56:08 am » posted from:Pune,Maharashtra,India

Thank you  very much.

I'll try and see how I can get best out of it.
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goldentrash
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 « Embed this message Reply #4 on: October 17, 2007, 03:12:11 am »

Hello Profesor
I know it's a bit rude but..I have a little time to give my teacher working java application of 2d collision of 2 balls inside the square fence and I need the source code..please if you can,help me.I'm a novice in java..so that's why I have a problem.
daniel
 « Last Edit: October 17, 2007, 03:31:49 am by goldentrash » Logged
Fu-Kwun Hwang
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 « Embed this message Reply #5 on: October 17, 2007, 08:29:01 am »

You can also "load ejs as signed applet" to view the code in EJS and recompile it or generate java source code from it.
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Chetmun
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 « Embed this message Reply #6 on: November 10, 2008, 07:39:34 am » posted from:Cleveland,Ohio,United States

Thank you for sharing your work on this 2D collision stuff. It was very clear and I was able to implement it quickly into my Java program. I have tested the technique with various parameters: 2 balls to multiple balls, different sizes, different initial trajectories, and different initial velocities. It worked well from the very beginning thanks to your clear example.

However, (didn't you know that was coming  ) I am having a bit of a problem. The balls seem to stick sometimes and even bounce off in odd directions. Sometimes the velocities increase at unexpected levels.

I put a test after the new locations and velocities have been calculated to see if the values were NaN's according to Java. In those cases I did not update the locations or velocities and the balls would overlap for a period of time.

I am assuming this is some kind of math precision issue. I have kept all variables at the level of Java's "double". Is there some kind of technique you employ to prevent this sort of behavior? Perhaps there's a flaw in my processing of all the balls. I "move" them all, then check each one against each other (only once, no redundancy) adjusting the locations and velocities according to your example.

Thanks in advance for any help.
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Fu-Kwun Hwang
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 « Embed this message Reply #7 on: November 11, 2008, 08:55:27 pm »

1. The situation will happen if you did not move the ball back to the time where two balls just collide. (If you just checked if those two ball collide with each other).
2. If you did the time correction. The situation you have descrbed might happened if the velocity was set too large or the time step is too large. And it also possible that you might have three balls collide at the same time (within your simulation time step).  However, the program only take care of two balls collision. Reduced the time step might help.

Because I do not know how it was implemented in your program and what are the initial condition for your case, I can not say any more.
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Chetmun
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 « Embed this message Reply #8 on: November 12, 2008, 01:18:15 am » posted from:Painesville,Ohio,United States

Thanks for your reply. I am enclosing my code for your perusal. I think I have included everything I've seen from your posts. In other words, I believe I have "moved" the balls back in time properly. I see your point about the velocities possibly being too large. I will experiment with that. The initial directional velocities are randomly between 13 and 20 per time step. The radii are randomly between 15 and 50. Even though I have multiple balls moving simultaneously, the situation arises with 2-ball collisions and no other ball nearby. Perhaps you can spot something I missed.

Code:
private boolean collision(Circle c1, Circle c2)
{
double x1 = c1.getX(), y1 = c1.getY();
double x2 = c2.getX(), y2 = c2.getY();

double dx = x2 - x1;
double dy = y2 - y1;
double d = Math.sqrt(dx*dx + dy*dy);

if(d <= r1 + r2)
{
double vx1 = c1.getXdir(), vy1 = c1.getXdir();
double vx2 = c2.getXdir(), vy2 = c2.getXdir();
double mass1 = c1.getMass(), mass2 = c2.getMass();

// velocity in the direction of (dx, dy)
double vp1 = (vx1*dx + vy1*dy) / d;
double vp2 = (vx2*dx + vy2*dy) / d;

// collision should have happened dt before
double dt = (r1 + r2 - d) / (vp1 - vp2);

// move the circles backward in time
x1 -= vx1 * dt;
y1 -= vy1 * dt;
x2 -= vx2 * dt;
y2 -= vy2 * dt;

// new collision calculations at impact
dx = x2 - x1;
dy = y2 - y1;
d = Math.sqrt(dx*dx + dy*dy);

// unit vector in the direction of the collision
double ax = dx/d;
double ay = dy/d;

// projection of the velocities in these axes
double va1 =  vx1*ax + vy1*ay;
double vb1 = -vx1*ay + vy1*ax;
double va2 =  vx2*ax + vy2*ay;
double vb2 = -vx2*ay + vy2*ax;

// calculate new velocity after collision
double ed = 1;
double vaP1 = va1 + (1 + ed) * (va2 - va1) / (1 + mass1/mass2);
double vaP2 = va2 + (1 + ed) * (va1 - va2) / (1 + mass2/mass1);

// undo projections
vx1 = vaP1*ax - vb1*ay;
vy1 = vaP1*ay + vb1*ax;
vx2 = vaP2*ax - vb2*ay;
vy2 = vaP2*ay + vb2*ax;

// move time dt forward
x1 += vx1 * dt;
y1 += vy1 * dt;
x2 += vx2 * dt;
y2 += vy2 * dt;

// update locations and velocities
if (!Double.isNaN(x1)) c1.setX(x1);
if (!Double.isNaN(y1)) c1.setY(y1);
if (!Double.isNaN(x2)) c2.setX(x2);
if (!Double.isNaN(y2)) c2.setY(y2);
if (!Double.isNaN(vx1)) c1.setXdir(vx1);
if (!Double.isNaN(vy1)) c1.setYdir(vy1);
if (!Double.isNaN(vx2)) c2.setXdir(vx2);
if (!Double.isNaN(vy2)) c2.setYdir(vy2);

return true;
}
else
return false;
}
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Chetmun
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 « Embed this message Reply #9 on: November 12, 2008, 09:02:13 am » posted from:Cleveland,Ohio,United States

P.S. I did notice an error in my code regarding the retrieval of the y-velocities and have fixed that to no avail. I'm going to try moving the balls further ahead in time to where they are no longer colliding. I think that is the problem. Not sure how to calculate that but it seems the thing to do.
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Chetmun
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 « Embed this message Reply #10 on: November 12, 2008, 09:19:57 am » posted from:Cleveland,Ohio,United States

To interested parties, I changed the if(d <= r1 + r2) to while(d <= r1 + r2) and it seems to work a little better. The balls don't seem to stick together. However, I'm still getting some odd jumps in velocity and the deflection angles look wrong sometimes.
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lookang
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 « Embed this message Reply #11 on: November 12, 2008, 04:26:20 pm » posted from:Singapore,,Singapore

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Fu-Kwun Hwang
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 « Embed this message Reply #12 on: November 12, 2008, 10:47:59 pm »

Quote
The initial directional velocities are randomly between 13 and 20 per time step. The radii are randomly between 15 and 50.

It seems that your time step is too large (or velocity is too large).
Because you have particle moves 13-20 unit per time step, however, the radii are between 15-50.
So it is possible that the particle could move past half of the size of the particle.
However,  an approximation was made when I calculate the time particles really collide. (I have assumed that when we detect particle collide, the overlap distance is much small that their radii.
I think your problem will not occur again if you change velocity to 1.3-2.0
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Chetmun
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 « Embed this message Reply #13 on: November 13, 2008, 04:06:34 am » posted from:Eastlake,Ohio,United States

Thank you, I will experiment with a reduction in the velocities though I am not convinced that will help regarding the "jumpiness" I am seeing. I have taken the randomness out and am just manipulating 3 circles of equal size but I still see the circles move in unexpected ways occasionally upon collision, ie. the wrong angle or with a much larger velocity. I am curious about the approximation you mention. How is it an approximation? I wonder if making it more exact would help.
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Fu-Kwun Hwang
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 « Embed this message Reply #14 on: November 13, 2008, 02:01:09 pm » posted from:Taipei,T'ai-pei,Taiwan

Quote
double vx1 = c1.getXdir(), vy1 = c1.getXdir();
double vx2 = c2.getXdir(), vy2 = c2.getXdir();

Please check out how you calculate vy1 and vy2!
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Chetmun
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 « Embed this message Reply #15 on: November 17, 2008, 05:59:08 am » posted from:Cleveland,Ohio,United States

Yes, thank you. I mentioned I had fixed that in Reply #9. I'm slowing everything down and adding lots of extra drawing and displaying of various values along the way. Something is definitely not right. I'll get to the bottom of it and let you all know what I find! It's a little cumbersome, code-wise, due to the fact that the drawing for each ball is in the ball class and the timer, the moving, and the repainting are separate java methods.
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 « Embed this message Reply #16 on: November 19, 2008, 12:33:44 am » posted from:Kalispell,Montana,United States

Chetmun, currently I'm working on a project also involving 2d collision, your private Boolean collision function has helped a great deal in understanding how to start. However, things become cloudy when the Circle class functions come into play. It would help me a great deal if I could take a peak at your Circle Object code? Sorry if this is asking too much, pseudo code would suffice as well... In general I'm stumped on what exactly is needed to represent a circle traveling through space. Thank you.
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Fu-Kwun Hwang
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 « Embed this message Reply #17 on: November 19, 2008, 04:00:43 pm » posted from:Taipei,T'ai-pei,Taiwan

The above simulation was generated with EJS.
There is another verison of 2D Collision , you can download the file and find out the original java code (written with JDK1.0.2).
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ozgurvt
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 « Embed this message Reply #18 on: December 28, 2008, 11:20:55 pm »

I couldn't understand what you are writing in the code, I hope you will explain the important parts with comments next time.

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Fu-Kwun Hwang
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 « Embed this message Reply #19 on: December 29, 2008, 08:30:25 am »

Please check out 2D Collision for related discussion.

You need to understand the physics before you can understand the code.
and the code you do not understand, otherwise, I will not be able to help.
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ArdTraveller
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 « Embed this message Reply #20 on: January 06, 2009, 06:46:33 pm »

Sir, can I please have the source code for this applet,even cooler than the other 2D collision, thx
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Fu-Kwun Hwang
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 « Embed this message Reply #21 on: January 06, 2009, 08:23:47 pm »

You can always download the EJS source cod in this forum if you login to the system.
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ArdTraveller
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 « Embed this message Reply #22 on: January 08, 2009, 09:59:02 am »

I'v succesfully gotten to run the EJS and the 2D collision simulation can run but it's in XML so could you provide me with the Java source code like the one provided for the 1D collision coz I don know how to generate the Java source code from the EJS.
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Fu-Kwun Hwang
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 « Embed this message Reply #23 on: January 08, 2009, 10:59:18 am » posted from:Taipei,T'ai-pei,Taiwan

There is a setting in EJS that allow you to either keep java code or remove java code after ejs class files were generated.
(I believe the default is keep java code).
You can find java code in the generated directory (ejsfilename +".app")
It is under _simulation for EJS version 3, under workspace/output/users/... for EJS version 4.

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ArdTraveller
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 « Embed this message Reply #24 on: January 08, 2009, 11:49:11 pm »

Well thank you sir but i still have a problem, the code needs a certain package because I can't compile and run it coz the main class which is Collision2D_e, extends this right ..org.opensourcephysics.ejs.AbstractModel and so with the other java programs so i don what to do it just can't run without this org package
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lookang
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 « Embed this message Reply #25 on: January 09, 2009, 08:33:35 am » posted from:Singapore,,Singapore

2. click on edit options button
3. a pop up on EJS options appears, first tab uncheck tickbox remove java files after compiling
4. the default is to remove for this file
5. use your computer explorer to goto F:\EasyJavaSimulation\EJS_4.1_081216\EJS_4.1\workspace\output\Collision2D_e.java  location may defer depend on what you expanded EJS.
6. i assume u are using EJS 4.1, for EJS 3.47, the idea is similar

try it!

i may be able to make a screenvideo by this weekend! watch this space for it!
Qn:How to watch this space?
under Additional Options... Notify me of replies. select it

Help U:
i have attached for you incase your unusually problem
"I can't compile and run it coz the main class which is Collision2D_e, extends this right ..org.opensourcephysics.ejs.AbstractModel and so with the other java programs so i don what to do it just can't run without this org package"

is bugging you.

Suggestion:
"I can't compile and run it coz the main class which is Collision2D_e, extends this right ..org.opensourcephysics.ejs.AbstractModel and so with the other java programs so i don what to do it just can't run without this org package"

remember to attribute your derived work like one of these
 « Last Edit: January 09, 2009, 08:42:46 am by lookang » Logged
Fu-Kwun Hwang
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 « Embed this message Reply #26 on: January 09, 2009, 05:56:24 pm » posted from:Taipei,T'ai-pei,Taiwan

Quote
Well thank you sir but i still have a problem, the code needs a certain package because I can't compile and run it coz the main class which is Collision2D_e, extends this right ..org.opensourcephysics.ejs.AbstractModel and so with the other java programs so i don what to do it just can't run without this org package

EJS will generate all the java class files and pack it into jar for you.
I  do not understand why you need to compile it again.
If you really need to do it, you will find osp.jar,ejs.jar... under ejs/bin

Please write down what is your final goal? May be there is some other easy way to do it (Not the way you were doing right now.)
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ArdTraveller
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 « Embed this message Reply #27 on: January 12, 2009, 09:24:35 am »

The thing is actually like this sir, i need a source code where i can use on my desktop and see it run on the desktop and actually just see the applet without having to create it into xml and jar and so on, just to see it run after the code is written in netbeans. The problem is the program has to import this org.colos.ejs.library._EjsConstants package which I don know where it is and then in the code there is this line static public String _getEjsModel() { return "./Collision2D_e.xml"; which if by using EJS would run but if just written in netbeans would not.
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Fu-Kwun Hwang
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 « Embed this message Reply #28 on: January 12, 2009, 01:29:58 pm » posted from:Taipei,T'ai-pei,Taiwan

If you just want to run it on the desktop.
The program will run nicely if you have java run time installed. You do not need the xml files.
You already have everything to run the java application.
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ArdTraveller
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 « Embed this message Reply #29 on: January 13, 2009, 02:15:43 pm »

I was able to run it in jar sir, i just really need ur help of providing the source code like the one you provided for the 2D Collision at this url http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=4 for this collision simulation, i was able to compile and run the one you gave for the 2D Collision, because the main function didn't have to extend any other package, if possible could you send it to this email, tera_xollaravo@yahoo.com, appreciate it much.
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You cannot always have happiness but you can always give happiness. ..."Mother Teresa(1910-1997, Roman Catholic Missionary, 1979 Nobel Peace Prize)"