The geodesic as well as the geodesic deviation equation for impulsive
gravitational waves involve highly singular products of distributions
(\theta\de, \theta^2\de, \de^2). A solution concept for these equations
based on embedding the distributional metric into the Colombeau algebra of
generalized functions is presented. Using a universal regularization procedure
we prove existence and uniqueness results and calculate the distributional
limits of these solutions explicitly. The obtained limits are regularization
independent and display the physically expected behavior.Comment: RevTeX, 9 pages, final version (minor corrections, references added