# Tagged Questions

**0**

votes

**0**answers

155 views

### Variational Problem v.s. Initial Value Problem

Is there a way to relate the variational problem where one specifies $x$ initially and finally to the initial value (Cauchy) problem where one specifies both $x$ and $p$ initially? As an example, ...

**4**

votes

**1**answer

219 views

### Minimizing action squared versus action

I have a very basic question in the calculus of variations:
Suppose I want to minimize the functional
$$A[r, r'] = \int_\Omega L(r, r') dx $$
When is it possible to say that extremals of $A$ agree ...

**10**

votes

**2**answers

1k views

### Surface equivalent of catenary curve

A catenary curve
is the shape taken by an idealized hanging chain or rope under the influence
of gravity. It has the equation $y= a \cosh (x/a)$.
My question is:
What is the shape taken by an ...

**7**

votes

**1**answer

661 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 $\hat g := \sqrt g$ ...

**4**

votes

**2**answers

459 views

### Minimal surface which divides a convex body into two regions of equal volume

Question. Given a convex body $\Omega$, what is the shape of a surface $\Gamma$ of minimal area which divides $\Omega$ into two regions of equal volume?
Background/motivation.
A 2D version of ...