Eikonals

Hello, spr!

Here are some questions that may stimulate debate here.

1: Does light follow a geodesic or an eikonal? I worked out a simple
case from point A in empty space to point B in a refracting medium, at
an incidence that would not cause TIR. I found the path light would
take to be the fastest, not the shortest path from A to B.

2: Given a plane tilted from normal to local gravity, a ball that can
roll on the plane, and points A and B on the plane. Assume B on a
strike to A, that is, B and A at the same altitude, but distinct. These
are terms from civil engineering. Strike is normal to dip, if I
remember right. Assume the ability to impart a single initial impulse
to the ball, of any magnitude and direction. This initial impulse has
magnitude mv and associated initial kinetic energy 1/2 m * v^2, and
results, in the interesting cases, in a trajectory from A to B, with
time t. Minimize the product E*t.

3: Given a piece of terrain, with analytic characteristics as follows:
continuous and continuously differentiable at every point, finite in
extent, and finite in variation from the mean altitude, is there an
eikonal between points A and B on this terrain for a bicycle? Make some
assumptions about bicycles and discuss. You might choose to minimize
E*t, for an "E-eikonal".

What I am doing here is working on a smart bike. 12VDC interfaces to
power many but not all GPS, PDA, and laptops are available, but 110 VAC
interfaces are ubiquitous. I have ordered a 600 W rating front drive
hub of brushed, gearless design for my experiments, and have regulators
and inverters coming out my ears. This hub will be used as a generator.


My goal is to supply small amounts of 110 VAC to various technologies
to inform, not propel the rider. We may assume the rider has the intent
and priorities of a bicycle courier, but the application is actually
military.

A small SEIG is under development but successful small, slow SEIGs are
rare, so for now, the generator/inverter option provides best hopes for
success.

I'll post a video link tomorrow. I have to catch a ride to work now.
How ironic....

Yours,

Doug Goncz
Replikon Research
Seven Corners, VA 22044-0394

.

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