2022年7月26日 · 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.

2022年4月14日 · 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 ...

2022年4月7日 · 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 $\mathcal{S}$.

2014年12月21日 · 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.

2021年7月28日 · 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.

The angular velocity of the disk has two contributions, the component $\vec\omega'$ due to the spin and the component $\vec\omega''$ due to a rotation of the inclined disc about a vertical axis. The latter corresponds to the wobbling as viewed by someone in the Earth frame.

2019年1月11日 · It explains that The expressions for the torque in the rotating and inertial frames are related by $\mathbf M_{inert} = \mathbf Q \mathbf M$ where $\mathbf Q$ is the rotation tensor (not rotation matrix), an orthogonal tensor related to the angular velocity vector by $${\displaystyle {\boldsymbol {\omega }}\times {\boldsymbol {v}}={\dot ...

The other twelve Euler-like sequences involve rotations about three distinct axes. You intrinsic ZYX sequence represents one of these twelve Tait-Bryan sequences. There are six intrinsic and six extrinsic Tait-Bryan sequences. Any one of these 24 Euler-like rotation sequences will obviously yield some proper orientation in three dimensional space.

2021年6月23日 · $\begingroup$ 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 ...

2024年1月24日 · 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). Is there some physics behind this? Is the amplitude just $0$ when this instant comes, or is this just an ilusion because our eyes cannot percieve this small oscilations?