Re: "Negotiating" a curve. EUREKA?

[John Denker <jsd@MONMOUTH.COM>]

At 12:03 PM 11/7/99 -0500, Ludwik Kowalski wrote:

> The last think I want to do is to include the gyroscopic effects.
> On the contrary, I want to eliminate everything but the most
> essential. Yes the wheels of the tricycle are massless.

OK

> So what is the problem?

I don't know!  I don't see a problem at all.

> The issue is to explain this in terms of an FBD (free body
> diagram). How to explain the net force in terms of individual
> external forces?

Why doesn't the most obvious diagram do it?

Start with a non-turning tricycle, heading north, but pushed from a funny
direction, say, from the southeast.  Resolve the pushing force into a
northward component and a westward component.  Observe that the westward
component is balanced by a force of constraint.  The northward component is
available to push the tricycle in the only direction it can go.

Now apply the same logic to the turning tricycle.  Apply it to each wheel
separately.  Each back wheel moves tangent to the circular path _at that
point_ and the front wheel moves tangent to the circular path _at that
point_ which is a significantly different point.  For any given setting of
the steering angle, for any given length of wheelbase, there is only one
circle that meets the requirements.  So the tricycle moves along that
circle.  At the CM or any other point(s) you choose, resolve the applied
force(s) into components along and against the constraints.

If this analysis isn't good enough, please explain why not.  Please be as
specific as possible.