The jamb (self-locking) process in three-dimensional collisions

For collisions that can be described by means of Routh's incremental model, the jamb or self-locking process, which is characterized by a negative slope of the plot of the normal (separating) velocity upsilon(n) as a function of the normal impulse P-n, is far more complicated in three dimensions than in planar collisions because its occurrence depends not only on the friction coefficient mu but also on the direction of sliding sigma, which is variable. A thorough study of the jamb process as it occurs in Routh's model is presented. For a given collision configuration the system behavior concerning jamb can be fully characterized in the plane of vectors mu sigma, where four jamb-related domains are defined. Jamb is investigated in the plane of the sliding velocity-where it occurs in an angular sector-and in the upsilon(n)(P-n) plots. When jamb starts during expansion, upsilon(n) > 0, a second compression-expansion phase can take place in some cases, and then the usual energetical restitution coefficient e(w) may be ill-defined. A new formulation for the energy dissipated by the normal force is presented that can be consistently applied in all cases. The new concepts and procedures are illustrated by means of an application example.