A short document discusses the general
problem of mathematical modeling of
the three-dimensional rotational dynamics
of rigid bodies and of the use of Euler
parameters to eliminate the singularities
occasioned by the use of Euler angles in
such modeling. The document goes on
to characterize a Hamiltonian model,
developed by the authors, that utilizes the
Euler parameters and, hence, is suitable
for use in computational simulations that
involve arbitrary rotational motion. In
this formulation unlike in prior Eulerparameter-
based formulations, there are
no algebraic constraints. This formulation
includes a general potential-energy
function, incorporates a minimum set of
momentum variables, and takes an
explicit state-space form convenient for
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