A new comprehensive derivation of normal form maps for grazing bifurcations in piecewise-smooth flows is presented. This links grazings with so-called border-collisions in piecewise-smooth maps. Contrary to previous literature, piecewise-linear local maps are derived only at non-smooth discontinuity boundaries. All other maps have either square-root or (3/2)-type singularities.
Additional information: Preprint of a paper later published by the American Physical Society (2001), Physical Review Letters, 86(12), pp.2553-2556, ISSN 0031-9007