Maciejewski - Dealing with the Ill-Conditioned Equations of Motion for
Articulated Figures

Maciejewski's paper tackles the issue of trying to solve numerically
difficult linear systems of equations that formulate kinematics and dynamics
of a rigid figure.  He first attempts to explain the nature of the
difficulty in finding such solutions and illustrates that the difficulties
arise more from the structure of an object rather than the formulation, and
proposes a means of measuring the severity of an ill-conditioned problem
with singular value analysis.  The second half of the paper deals with
finding physically meaningful solutions to these types of problems.  To
these ends, Maciejewski proposes a damped least-squares formulation of the
quantities being integrated in the kinematic and dynamic simulations.  Once
again, my understanding of this paper suffers from the level of mathematical
abstraction present in his illustrations of the problem.