  Particles at rest before the arrival of a burst of gravitational wave move,
after the wave has passed, with constant velocity along diverging geodesics. As
recognized by Souriau 50 years ago and then forgotten, their motion is
particularly simple in Baldwin-Jeffery-Rosen (BJR) coordinates (which are
however defined only in coordinate patches): they are determined when the first
integrals associated with the 5-parameter isometry group (recently identified
as L\'evy-Leblond's ``Carroll'' group with broken rotations) are used. A global
description can be given instead in terms of Brinkmann coordinates, however it
requires to solve a Sturm-Liouville equation, whereas the relation between BJR
and Brinkmann requires to solve yet another Sturm-Liouville equation. The
theory is illustrated by geodesic motion in a linearly polarized (approximate)
``sandwich'' wave proposed by Gibbons and Hawking for gravitational collapse,
and by circularly polarized approximate sandwich waves with Gaussian envelope.
