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15
votes
6answers
2k views

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 ...
20
votes
3answers
2k views

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 ...
1
vote
0answers
804 views

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?
15
votes
2answers
2k views

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 ...
14
votes
8answers
2k views

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 ...
86
votes
0answers
6k views

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 ...
6
votes
3answers
369 views

Do there exist small neighborhoods in a classical mechanical system without pairs of focal points?

The question I will ask makes sense in much more generality, but I will leave the translation to the experts, since I'm only looking for a special case (and it would not surprise me if the answer does ...
9
votes
3answers
334 views

Surfaces that are 'everywhere accessible' to a randomly positioned Newtonian particle with an arbitrary velocity vector

Consider an idealized classical particle confined to a two-dimensional surface that is frictionless. The particle's initial position on the surface is randomly selected, a nonzero velocity vector is ...