Smooth dynamics of oblique impact with friction

Effects of friction during impact between hard bodies can be analysed as a continuous function of the normal component of impulse p; i.e. by considering the normal component of impulse as an independent variable. The resulting expressions for changes in relative velocity at the contact point C, are obtained as a continuous function vC(p). Any sliding during contact is opposed by Coulomb friction. In this analysis the terminal normal component of impulse pf separates into an initial ‘period’ of compression or approach followed by a ‘period’ of expansion or restitution. For planar impact where initial slip is brought to rest before termination of impact, the tangential component of impulse separates into a ‘period’ of initial sliding and a subsequent ‘period’ of either reverse sliding or stick.For oblique planar impact in general, initial sliding can continue in the original direction or else slow and come to rest before separation. After initial sliding is brought to rest, subsequently either the direction of sliding reverses or, with a sufficiently large coefficient of friction, the contact sticks. Regions for each pattern of sliding are mapped as functions of the initial angle of incidence, the coefficient of friction and the inertia properties of the colliding bodies. This mapping employs two non-dimensional parameters; (1) a normalised initial angle of incidence and (2) a parameter which depends on the unbalance of the configuration as well as the coefficient of friction. With these new impact parameters, terminal velocities and energy dissipation are calculated as functions of the normalised angle of incidence but independent of the impact speed. Furthermore, specific relationships are obtained between the kinematic, kinetic and energetic coefficients of restitution. For frictional impact of bodies in an eccentric configuration, it is shown that these definitions are equivalent only if sliding is unidirectional.

► Analytical method which maps different patterns of sliding as function of normalised angle of incidence.
► Solution depends on (1) normalised angle of incidence, (2) unbalance of the configuration.
► With these parameters, terminal velocities and energy dissipation are independent of impact speed.
► Specific relationships obtained between kinematic, kinetic and energetic coefficients of restitution.
► For frictional impact, these COR definitions are equivalent only if sliding is unidirectional.