from  Aircraft Landing Gear Design: Principles and Practices by Norman
S. Currey:

9.5 Castering Nose Wheels

.......

Configurations a and b in Fig 9.24 are statically neutral and
dynamically stable in both forward and aft movement. In the latter
configiration, the wheel swivels 180 deg for aft movement.  A shimmy
damper is resuired for both configurations unless corotating wheels are
used.

Configuration c is statically and dynamically stable in both forward and
reverse and also requires shimmy damping except, posibly, when t =
R-1.2R.

Configuration d is statically unstable and dynamically stable.  It is
unstable in reverse and the gear must be locked ot steered for this
operation.  Shimmy damping is required.  This configuration is often
used for tail wheels, using friction to provide shimmy damping.


illustration at:

http://www.mykr2.com/90437.pdf




jg



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