Re: gimbal lock

["John S. Denker" <jsd@MONMOUTH.COM>]

Last year (2000) there was issued a patent for
a particular improvement in a method for using
quaternions to deal with gimbal lock (or the
software equivalent thereof):

http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=/netahtml/srchnum.htm&r=1&f=G&l=50&s1='6,061,611'.WKU.&OS=PN/6,061,611&RS=PN/6,061,611

Start reading where it says:

> 1. Field of the Invention
>
> The present invention relates in general to inertial navigation systems (INS), and more
> particularly to a kinematics equations integrator device and method for obtaining the
> attitude of a vehicle from the closed-form integration of kinematics equations utilizing a
> four-dimensional operator such that the magnitude of said four-dimensional operator is
> always equal to unity.
>
> 2. Background Art
>
> Inertial navigation systems (INS) are widely used in several flight vehicle applications such
> as aircraft, missiles, spacecraft and satellites. These self-contained navigation systems
> determine the attitude or position of the flight vehicle relative to some reference coordinate
> frame. The INS works by integrating the angular velocity or rates of acceleration,
> measured by onboard sensors, to obtain position with respect to a body-centered
> coordinate frame.

... and the rest of it is quite a good read IMHO.

============

You might want to bookmark this for possible use the
next time a student asks why bother learning physics.
Hasn't all the good physics been done already?  Well,
no, there are still very interesting, very practical
questions out there that can't be solved unless you
understand some physics (and some other things).