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Give some description about degenerate stadia manipulations. #66

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14 changes: 10 additions & 4 deletions main.tex
Original file line number Diff line number Diff line change
Expand Up @@ -403,10 +403,16 @@ \subsection*{Departures from Yeadon's work}
circle. This scenario is not discussed by Yeadon.
\item[Degenerate stadia] In the case where a stadium has zero thickness (a
circle), the stadium is degenerate and some equations have a zero in the
denominator. In this scenario, Yeadon still employs the formulae for
stadium solids but sets the thickness to be very
small~\cite{Yeadon1990f}. Instead, we manipulate the equations so that
the approximation is not necessary.
denominator; however, the resulting shape is still valid. In this
scenario, Yeadon still employs the formulae for stadium solids but sets
the thickness to be very small~\cite{Yeadon1990f}. Instead, we
manipulate the equations so that the approximation is not necessary. In
the case that only one of the stadia for a solid has zero thickness, the
divide-by-zero issue is removed by computing the mass properties for the
stadium solid in which the two stadia are swapped. However, this
manipulation does not work if both stadia have zero thickness; for this
case, we compute the inertial properties of a truncated cone; see code
for details.
\item[Joint center of chest-head segment] We locate the joint center
between the torso \textbf{T} and the chest-head \textbf{C} at the center
of level \textbf{Ls3}. This is in accordance with Figure 1 of
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