On 2013-10-08, Marshall, John <j.marshall at geos.com> wrote:
> The three parameters with uncertainty are Heave, Pitch and Roll, since
> they are "real" measurements from a sensor. Has anyone had experience
> of using maxima to calculate error propagation?
Maxima doesn't have anything to handle such problems specifically.
The simplest thing to do is linearize it (via derivatives) but if the
function (sine / cosine / whatever) is noticeably nonlinear over the
range of the uncertain variable (say more or less the middle 95% of
mass) then linearization will be a poor approximation. This is going
to be especially noticeable since sine / cosine have bounded ranges --
anything near the edges of the range will be "interesting" (i.e. not
anywhere near linear).
Just glancing at the equation, my guess is that an exact solution, if
possible, is probably enormous and clumsy. As to approximations, the
easiest thing is a Monte Carlo method. If you just need to get a
result in the ballpark, that's my recommendation. Semi-numerical,
probably more nearly exact approaches are also possible -- I can give
you some ideas if you're interested.
Hope this helps,
Robert Dodier