# Tagged Questions

**3**

votes

**0**answers

38 views

### Weinstein's local classification of Lagrangian foliations

In the paper "Symplectic manifolds and their Lagrangian submanifolds", Weinstein showed that locally all the Lagrangian foliations are symplectomorhic to the fiber foliation of a cotangent bundle.
I ...

**6**

votes

**1**answer

440 views

### Is there a sideways-walking rolling convex body?

Let $K$ be a solid, homogenous convex body in $\mathbb{R}^3$.
Place $K$ on an inclined plane, and let it roll down the plane,
under some reasonable assumptions of friction between $K$ and
the plane, ...

**8**

votes

**1**answer

370 views

### Oloid and sphericon: rolling develops entire surface

Wikipedia says that,
"The oloid is one of the only known objects, along with some members of the sphericon family, that while rolling, develops its entire surface."
Below are illustrations of ...

**-2**

votes

**2**answers

553 views

### Regarding understanding differential geometry [closed]

I am essentially looking for a book that would hold my hand through basic concepts to more complicated ones. I am coming from physics. I am looking to make some connections with Classical mechanics ...

**11**

votes

**5**answers

502 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 ...

**4**

votes

**0**answers

468 views

### Egg-ovoid rolling down an inclined plane

I am seeking a mathematical analysis of an egg-ovoid rolling down an inclined plane,
for pedagogical reasons.
It is well-known folk lore that the shape of an egg prevents it from rolling away from
...

**4**

votes

**2**answers

613 views

### References for the Poincaré-Cartan forms

Hello, everybody. I'm looking for some reference about the PoincarĂ©-Cartan form, I do not know how it is defined, I just know that it is used in Lagrangian mechanics but I have not found any ...

**10**

votes

**3**answers

658 views

### “Rolling Geodesics”: Designing a $k$-putt green

I am interested in what might be called rolling geodesics, paths
of physical particles confined to a surface in $\mathbb{R}^3$
under certain force conditions.
Here I will pose a specific (but ...

**12**

votes

**4**answers

1k views

### What is the role of contact geometry in the hamiltonian mechanics?

Let us assume someone is interested in the study of Hamiltonian mechanics.
What are good examples to illustrate him of the usefulness of contact geometry in this context?
On one hand the Hamiltonian ...

**15**

votes

**5**answers

936 views

### G-bundles in classical mechanics

The paper Geometry of the Prytz Planimeter described a mechanical instrument whose configuration space is an $S^1$-bundle with an $SU(1,1)$ action. That paper goes on to study the holonomies of ...

**8**

votes

**1**answer

678 views

### The rain hull and the rain ridge

Rain falls steadily on an island, a 2-manifold $M$, which you may
assume, as you prefer,
is: (a) smooth, or (b) a PL-manifold, or perhaps even
(c) a
triangulated irregular network (TIN).
After a ...

**10**

votes

**5**answers

980 views

### reference for Noether's theorem

What is a good reference for a geometric version of Noether's theorem about Lagrangians, symmetries and conserved currents?

**7**

votes

**1**answer

724 views

### Calculating the geodesic equation for a particular set of phase-space coordinates

Let $g$ be a Riemannian metric on the $d$-dimensional flat space $\mathbb R^d$, and consider the usual Lagrangian $$L(x, \dot x) = \tfrac 1 2 g_{ij}(x) \dot x^i \dot x^j.$$ Let $\hat g := \sqrt g$ ...

**19**

votes

**1**answer

755 views

### Which convex bodies roll along closed geodesics?

An ellipsoid could be rolled (without slippage) on a horizontal plane so that its point
of contact traces out a closed geodesic on its surface:
...

**5**

votes

**1**answer

500 views

### Rolling a convex body: Geodesics vs. rolling curves

What are the curves of contact on a convex body $B$ rolling down an inclined plane?
Assume $B$ is smooth, and there is sufficient friction to prevent slippage.
Certainly, one can develop a geodesic ...