Re: BEFORE "Negotiating" a curve.

[John Denker <jsd@MONMOUTH.COM>]

At 03:37 PM 11/9/99 -0500, Ludwik Kowalski wrote:

> Think about a floor made from tiny horizontal platforms supported
> supported by vertical springs "welded to the ground".

An excellent model.  Formulating model systems like that is a good way to
communicate.

> Suppose only
> 5 or 7 springs are in contact with the wheel at any given time, one is
> compressed to the maximums, two or three (those in front) being
> compressed and other two or three being (those behind) being
> decompressed. The decompressing springs work on the wheel while
> compressing springs are being worked upon by the wheel.

To achieve your stated goal of modelling dissipation, you need more than
springs.  I suggest each spring should have a shock-absorber
attached.  That way the energy leaving the wheel at the leading edge
exceeds the energy returning to the wheel at the trailing edge.

This will take energy and angular momentum out of the wheel.  To make sure
there is a corresponding reduction in linear momentum, we need to invoke
the constraint that the wheel rolls without slipping.

> By what
> mechanism does the "backward component" is produced while the
> floor is interacting with the rolling sphere or wheel?
...
> The floor particles (springs ?) are pushed down, not forward.

I strongly suggest you need your model springs to resist forward
push.  Otherwise your wheel wouldn't be constrained to roll -- it would
just slide along the road.  Imagine sandpaper glued to platforms on top of
the springs, giving infinite static friction against any sliding sideways
against the constraints *and* any motion (other than pure rolling) along
the constraint.

> Don't you think that this question must be answered before one can
> proceed with an analysis of the "road negotiation" by wheeled vehicle?

No.  Absolutely not.  There is a notion of "ideal wheel" which suffices to
answer your questions about negotiating a turn.  I say again an ideal wheel
offers unlimited resistance to any motion other than pure rolling.  If this
model isn't good enough, please explain why not.  Please be as specific as
possible.