Science > Physics > How to plot post-collision trajectories of 2 cylinders
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Science > Physics |
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"" |
| Date: |
03 Jun 2007 06:34:38 PM |
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How to plot post-collision trajectories of 2 cylinders |
Hi all,
Imagine two thin cylinders are flying through 3d space
toward each other. Each has a different mass and length;
each has its center of gravity at the middle of its length.
They will collide, but the collision may occur anywhere along
the length. Each is probably rotating while in motion at its own
speed, like two dowels simultaneously thrown at each other.
The collision is elastic.
How would one estimate how each will respond
to the collision?
Thanks.
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| User: "dlzc" |
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| Title: Re: How to plot post-collision trajectories of 2 cylinders |
04 Jun 2007 03:16:11 PM |
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Dear funnybunnyf...:
On Jun 3, 4:34 pm, wrote:
Hi all,
Imagine two thin cylinders are flying through 3d space
toward each other. Each has a different mass and
length; each has its center of gravity at the middle of
its length. They will collide, but the collision may
occur anywhere along the length. Each is probably
rotating while in motion at its own speed, like two
dowels simultaneously thrown at each other. The
collision is elastic.
How would one estimate how each will respond
to the collision?
I would consider the differences between your cylinder-cylinder
interaction, and one that occurs in the USA "national pastime"...
baseball. The interaction between a bat and a ball would be similar
for most configurations where the axes of the two cylinders are most
skew... so maybe 75% of your solution space could be contained /
modeled by such an approxmation.
Would that make it easier?
David A. Smith
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| User: "Thomas Smid" |
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| Title: Re: How to plot post-collision trajectories of 2 cylinders |
06 Jun 2007 09:31:53 AM |
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On 4 Jun, 00:34, wrote:
Hi all,
Imagine two thin cylinders are flying through 3d space
toward each other. Each has a different mass and length;
each has its center of gravity at the middle of its length.
They will collide, but the collision may occur anywhere along
the length. Each is probably rotating while in motion at its own
speed, like two dowels simultaneously thrown at each other.
The collision is elastic.
How would one estimate how each will respond
to the collision?
Thanks.
You should be able to treat this problem exactly. See for instance
http://www.myphysicslab.com/collision.html , ( this contains some
further complications that you can ignore however); unfortunately the
associated Java applet doesn't seem to work anymore (at least not in
my browser)).
Broadly speaking, I would generally expect that if you take the local
vertical at the point of impact and take the components of this vector
parallel and perpendicular to the direction from there to the center
of mass, then the former component should change the translational
momentum of the body and the latter the rotational.
Now since the local vertical on the side of a cylinder is always
perpendicular to the axis of the cylinder, it makes an angle
tan(theta)=d/r with the direction to the center of mass (where d is
the distance from the center of mass along the cylinder axis, and r
the radius of the cylinder). This means that for a thin cylinder
(r<<d), theta will always be close to 90 degrees, so the collision
should actually only change the rotation of the cylinder (unless you
manage to hit the cylinder either close enough to its center or on its
face).
Thomas
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