# Tagged Questions

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### Functional Analysis and its relation to mechanics

Hi I'm currently learning Hamiltonian and Lagrangian Mechanics (which I think also encompasses the calculus of variations) and I've also grown interested in functional analysis. I'm wondering if there ...
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### Generalizing square wheels rolling on inverted catenaries

It is not uncommon to see in a science museum a bicycle with square wheels that rides smoothly over a washboard-like surface made from inverted catenary curves (e.g., at the Münich museum). The ...
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### When sticks fall, will they weave?

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 ...
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### Catenary curve under non-uniform gravitational field

The catenary curve is the shape of a chain hanging between two equal-height poles under the influence of gravity. But the derivation of the (hyperbolic cosine) curve equation from the physics ...
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### Classical mechanics motivation for poisson manifolds?

Suppose I want to understand classical mechanics. Why should I be interested in arbitrary poisson manifolds and not just in symplectic ones? What are examples of systems best described by non ...
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### How to calculate the rolling resistance of a wheel over an obstacle? [closed]

Imagine a bicycle travelling at speed, and then rolling over a log. What are the principles behind calculating the force that is required to roll a wheel over an obstacle?
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### Fastest Rolling Shape?

The following questions occurred to me. This is not research mathematics, just idle curiosity. Apologies if it is inappropriate. Suppose you have a fixed volume V of maleable material, perhaps clay....
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### How can I conclude that I live in a solar system?

Well, this is an awkward question and I don't know if it is mathematical enough for MO (I'm sorry if not) but I'll try it: What observations in the coordinate system centered in my fixed position on ...
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### Dropping three bodies

Consider the usual three-body problem with Newtonian $1/r^2$ force between masses. Let the three masses start off at rest, and not collinear. Then they will become collinear a finite time ...