The classical-mechanics tag has no usage guidance.

**15**

votes

**6**answers

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

**3**answers

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

**0**answers

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

**2**answers

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

**8**answers

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

**0**answers

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

**3**answers

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

**3**answers

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 ...