  It is known that many peculiar nonlinear vibration problems in impacting
systems are caused by grazing incidences. Such bifurcation phenomena are
normally investigated through the Poincare map. The discrete-time map of a
simple impact oscillator was derived by Nordmark, which showed that there
should be a square-root singularity in the Jacobian matrix close to the grazing
condition. In this paper we show that the square root singularity will be
expressed only in the trace of the Jacobian matrix, while the determinant
remains invariant across the grazing condition.
