Jul 26, 2022 · I'm a physics student who got an interest in Euler's disks. As you may know, an Euler's disk is basically a big fat coin spinning upon a (smooth) surface. As the disk loses energy due to friction with air and with the surface itself, its precession frequency increases (theoretically diverging without bounds) until it stops.

Apr 7, 2022 · The disk $\mathcal{S}$ has a radius of $\cos \alpha$, so the center $\mathcal{C}$ should stay fixed (no horizontal translation of the center $\mathcal{C}$). See the picture below: If the moving disk $\mathcal{D}$ was sliding on the static disk $\mathcal{S}$, the point $\mathcal{A}$ would simply rotate around the border of $\mathcal{S}$.

Dec 21, 2014 · Accelerating the fluid requires a force just as accelerating any mass does. Spinning the Euler's disk in the fluid is going to require accelerating the fluid to move it around as the disk spins, and this will exert a force on the disk. So spinning the disk in superfluid helium is not the same as spinning it in a vacuum.

Apr 14, 2022 · From now on, taking the Assumption 1: that the center of mass of the disk only moves on the vertical line, so every time the disk is making a revolution the center of mass has to get lower by a little bit, so, the disk has extended a little bit flatter, so on each revolution the projection of the radius on the flat surface (referred from the ...

Jul 28, 2021 · After one revolution around the small radius, one wobble, the disk will not have rotated all the way around. If the black mark on the disk starts pointing down to the table, the "leftover part of the circumference" will be how far the black marker line now is from its start position - i.e. how far it moved due to the rotation.

Euler-Lagrange equations: Connections between the field theory and point mechanics Hot Network Questions Why is mechanical energy lost and linear momentum not conserved when a string suddenly becomes taut in a vertical two-mass system?

Jan 24, 2024 · as we see the oscilation amplitude decreases exponentially, but never is exactly zero. If you now go to real life, you will see that at one point in time, it will be completely stopped. Other example that comes to my mind is the Euler Disk, which spends lots of time moving but suddenly stops completely (same as with the pendulum).

Jun 23, 2021 · $\begingroup$ apart from the Euler-disk like motion at the end, I don't think there is any "pattern" arising here given the initial states. The ring acquires energy due to lowering of gravitational potential when it reaches the bottom most point on the surface, which helps it precess till it loses contact with the surface. the nature of the ...

Aug 13, 2021 · Consider a uniform thin disk that rolls without slipping on a horizontal plane. A horizontal force is applied to the center of the disk and in a direction parallel to the plane of the disk. (a) Derive Lagrange’s equations and find the generalized force. (b) Discuss the motion if the force is not applied parallel to the plane of the disk.

Derivation of Newton-Euler equations (2 answers) Closed 7 years ago . Sorry for using this image, but I thought this was the most convenient way of asking this question.