Formulation of rigid body impact problems using generalized coefficients

The equations of motion of a rigid body expressed in terms of impulse and momentum are linear. When applied to rigid body collisions, it is known that the equations of motion are insufficient to provide a solution of the classical impact problem; an additional equation is needed for each unknown impulse component. Using a set of coefficients, a problem formulation is presented that extends Newton's approach for collinear impacts of particles to three-dimensional impact problems Being linear and algebraic these equations can be solved, providing a set of solution equations in terms of the physical system parameters, initial conditions and the coefficients. A unique feature of these equations is that they are independent of the contact process(es) and apply to all collisions meeting the rigid body assumptions whether energy is or is not conserved (contact processes may involve the release of stored energy). Certain solution behavior, including the energy change can be found by treating the coefficients as parameters. By imposing work-energy and/or kinematic constraints, coefficients can be bounded to insure realistic solutions. Coefficients are defined for couple-impulses so the approach is not limited to point contact. Examples are given of the collision of a sphere against a massive barrier (surface). In one, the sphere has an initial cross spin (about its roll-spin axis) and the tangential process is Coulomb friction. Another, including experimental data, is for microspheres (approximate to 1-100 mu m diameter), where the dynamic contact processes are not fully understood. (C) 1997 Elsevier Science Ltd.