Re: "Negotiating" a curve. EUREKA?

[John Denker <jsd@MONMOUTH.COM>]

At 04:35 PM 11/6/99 -0500, Ludwik Kowalski wrote:
> John_D would probably say (and I was saying the
> same thing the other night) that forces in the bearing
> are internal and that only external forces matter.

Sometimes I would say that.  Gyroscopic precession can be considered a
consequence of "internal" forces, and there are cases where it matters.
But in this case it doesn't matter much.

> This
> would certainly be the case if the wheels were locked.
> Then I realized that wheels are not rigid and that the
> FBD can not be used, except for the rigid platform.
> I have to think about the situation again. Reading the
> books recommended by Leigh will be the first step.

I say again the non-rigidity is not essential to understanding the problem
as originally posed.

Suggestion:  start by considering the limit where the wheels have
negligible mass.  Then they contribute nothing to the kinematics, other
than to constrain the motion of the rest of the tricycle.

Indeed if the rolling motion of the wheels is keeping you from seeing the
kinematics of the original problem, replace the wheels by beads sliding on
wires (three straight wires for the non-turning case, and three curved
wires for the turning case).

=======

Of course the angular momentum of the wheel does contribute to the
kinematics, but
 a) for real tricycles this is a minor contribution, and
 b) it can easily be taken into account later if that level of detail is
really needed.

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com