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From: cgo@doc.ntu.ac.uk (Mr Chris Goodwin)
Subject: Truck backing up model or how long is a bent stick?
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Date: Mon, 23 Sep 1996 13:49:49 GMT
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Hello all,

	I'm trying to model the truck backing up problem, but I'm having
difficulty calculating the position of a truck for the next state.

ie. If I have a truck moving forward at speed v m/s, is currently at zero 
degrees orientation to the x-axis, is of length d, and has its steering wheel
at angle phi to the straight line, then what is its position after
one second (and its orientation) ?

	I can work out a formula, but I get some infinities which
cancel out when phi=0.0.  This isn't much good for a computer simulation since
I get divide by zero errors etc.  Can anyone suggest a solution which
doesn't have this problem?

Another way of stating the problem is:

	If I have a stick of length d clamped at its base and pointing
straight upwards, its tip could be said to be at (0,d).  If I push
the tip of the stick so that it bends evenly forming a smooth arc of
angle theta, what is the co-ordinates of the tip?  Again,
a solution is sought where there are no infinties which cancel.

many thanks for any help,

Chris Goodwin
cgo@doc.ntu.ac.uk

