The dynamics of clattering I: Equation of motion and examples

The "clattering" motion that results when flat objects, like portable electronic products, strikes the ground at an angle, is introduced and studied. During clattering one corner of the product touches down first, then successive corners strike one or more times, before it either bounces clear, or comes to rest on the floor. (This stands in distinct contrast to standard fragility tests which involve a single impact and no rotation.) The problem is formalized through the small-angle clattering of a unidimensional "bar" which contacts the ground only at its ends. Its equation of motion is constructed via transition matrices that govern the jumps in endpoint velocities from each collision. It is shown that the number and severity of the individual impacts experienced by the bar is highly variable, depending on mass distribution and coefficient of restitution. For several choices of these parameters, graphical results are presented for quantities that bear on shock-damage, such as: the total number of impacts, sequence of linear and angular velocity jumps, total time before clattering ends, total energy loss, peak linear impulse, etc. In particular, it is illustrated that parts of the bar can undergo a rapid sequence of "amplified" velocity reversals. A companion paper (Goyal et al., 1998b) outlines some global results, and practical implications for shock protection.