# Tagged Questions

501 views

### To what extent does trajectory determine gravity sources?

Suppose one has in-hand an accurate time-space trajectory in $\mathbb{R}^3$ of a (small) body, say an asteroid or satellite—effectively a point. To what extent does this trajectory determine the ...
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### Generalizing a square wheel to a body rolling on a surface

A square wheel rolling on a catenary road maintains the wheel center at a fixed height, a well-known construction previously discussed on MO (e.g., "Generalizing square wheels rolling on inverted ...
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### Functions approximated by rolling epicycle curves

Imagine a decreasing sequence of (positive) radii $r_1 > r_2 > r_3 > \cdots$ and a series of nested circles $C_1 \supset C_2 \supset C_3 \supset \cdots$ with these radii, initially each ...
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### Floating polyhedra with fair equilibria

Is there a homogeneous convex polyhedron which floats so that some subset (perhaps all) of its faces is distinguished as "up" (above the water line) in stable equilibrium, each face with ...
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### Which motion is exclusive in 3D or higher dimensions?

Hi guys, I have a simple question Linear movement can be found in 1D, 2D and 3D world objects Rotation can be found in 2D and 3D world objects. Now, are there any kind of motion can only be found ...
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### Fair but irregular polyhedral dice

I am interested in determining a collection of geometric conditions that will guarantee that a convex polyhedron of $n$ faces is a fair die in the sense that, upon random rolling, it has an equal ...
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### $\exists$ a shot in ideal pocket billiards?

Assume you have one shot with the cue ball in pocket billiards (a.k.a. pool), with the game idealized in that no spin is placed on the cue ball in the initial shot, all collisions between billiard ...
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### Hanging a ball with string

What is the shortest length of string that suffices to hang a unit-radius ball $B$? This question is related to an earlier MO question, but I think different. Assume that the ball is ...
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### Parabolic envelope of fireworks

The envelope of parabolic trajectories from a common launch point is itself a parabola. In the U.S. this weekend many will have a chance to observe this fact direcly, as the 4th of July is ...
Imagine $n$ $z$-vertical sticks uniformly spaced around a unit-radius circle in the $xy$-plane. At $t{=}0$, each is randomly $\epsilon$-perturbed from the vertical, and they fall under the influence ...