# Simulating a spinning/rolling disk

1. Jun 19, 2004

i am trying to create an animation simulating a coin spinning/rolling on a table top. how can the phyics involved over time be explained in an equation? any references (especially illustrated ones) would be helpful. thanks in advance!

2. Jun 20, 2004

### Gza

$$\vec{F} = m\vec{a}$$

Sorry for the smartass reply, but there are just too many ways to approach such a simulation, and unless this simulation is exceedingly simple, don't expect just one simple equation. Please be more specific of the details, and i'll be glad to help out.

3. Jun 20, 2004

### arildno

For this type of problem,
$$\vec{r}\times\vec{F}=\frac{d\vec{\mathcal{L}}_{G}}{dt}$$
is probably "far more important".
I believe Euler did some initial work on this; but it is still a very difficult problem.
The problem is, I believe, that the frictional torque from the table generates
a very difficult rotational mode for the coin.

Last edited: Jun 20, 2004
4. Jun 20, 2004

some illustrations may help

thanks for the help!

here's a quick example of the idea: http://www.geocities.com/atadami/disk.gif

this animation is not accurate to the laws of physics. i just tried to make it look close. to achieve this i manually shortened the disk's distance from the origin (radius) as i rotated it around the origin and increased the disk's bank properties as it rotated towards the origin. i also had to manually lower the disk so it would remain on the table (see explanation below).

my trouble is that the disk is being "controlled" about it's pivot point which is its center point. therefore, as the disk is banking (tilting as it slows down) the lower edge of the disk ends up coming off of the table.
look at this: http://www.geocities.com/atadami/side.gif i need to figure out the equation(s) to make the pivot point lower as the coin banks.

i've also done some experimenting with: $$r=ae^{b\theta}$$ and was able to create a Logarithmic Spiral path for the disk.
i'm not trying to animate or simulate euler's spinning disk... more rolling... no spinning.... sorry if this makes no sense...

5. Jun 20, 2004

### arildno

atadami; Yahoo won't allow others to see your results in this manner

6. Jun 20, 2004

### Gokul43201

Staff Emeritus
If you want rolling without slipping, your constraints are :

$$dx - asin\theta d\phi = 0 = dy + acos\theta d\phi$$

$$\theta$$ is the angle in the x-y plane made by the point of contact,
$$\phi$$ is the angular rotation of the disc about its central axis, and
'a' is the radius of the disc.

I would solve the Lagrangian with these constraints, to get the equations of motion. You will need to supply initial conditions to get particular solutions.

7. Jun 20, 2004