This paper presents a complete study on the collision with friction of one or two rigid bodies without constraints. The differential formula between the velocities and impulse uses the notion of inertance resulting from the theory of screws (Plückerian coordinates). One thus may calculate the kinematic and dynamic parameters, the velocities and the kinetic energies of the two rigid solids after the collision, and the variation of the kinetic energy. The calculation is detailed for the Newton, Poisson, and energetic variants of the coefficient of restitution. The variation of the kinematic and dynamic parameters in relation to the coefficient of restitution and coefficient of friction for all the three variants are presented and discussed. A numerical example highlights the theory.
PandreaNStănescuN-D. A new approach in the study of frictionless collisions using inertances. Proc IMechE, Part C: J Mechanical Engineering Science2015; 229: 2144–2157.
2.
BatlleJA. Termination condition for three-dimensional inelastic collisions in multibody systems. Int J Impact Eng2001; 25: 615–629.
3.
BatlleJACardonaS. The jamb (self locking) process in three-dimensional collisions. ASME J Appl Mech1998; 65: 417–423.
4.
BrogliatoB. Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction. Multibody Syst Dyn2014; 32: 175–216.
5.
GlockerC. Energetic consistency conditions for standard impacts. Part I: Newton-type inequality impact laws. Multibody Syst Dyn2013; 29: 77–117.
6.
GlockerC. Energetic consistency conditions for standard impacts. Part II: Poisson-type inequality impact laws. Multibody Syst Dyn2014; 32: 445–509.
BrachRM. Friction restitution and energy loss in planar collision. ASME J Appl Mech1984; 51: 164–170.
9.
BrachRM. Rigid body collision. ASME J Appl Mech1989; 56: 133–138.
10.
DimentbergF. The theory of screws and its applications, Moscow: Nauka, 1978.
11.
ElkaranshawyHA. Rough collision in three-dimensional rigid multi-body systems. Proc IMechE, Part K: J Multi-body Dynamics2007; 221: 541–550.
12.
FloresPAmbrósioJClaroJCPet al.Influence of the contact-impact force model on the dynamic response of multi-body systems. Proc IMechE, Part K: J Multi-body Dynamics2006; 220: 21–34.
13.
KapoulitsasMG. On the collision of rigid bodies. J Appl Math Phys (ZAMP)1995; 46: 709–723.
14.
KellerJB. Impact with friction. ASME J Appl Mech1986; 53: 1–4.
15.
LankaraniHMPereiraMFOS. Treatment of impact with friction in planar multibody mechanical systems. Multibody Syst Dyn2001; 6: 203–227.
16.
MarghituBDHurmuzluY. Three-dimensional rigid body collisions with multiple contact points. ASME J Appl Mech1995; 62: 725–732.
17.
PandreaN. On the collisions of solids. Stud Res Appl Mech1990; 40: 117–131.
18.
PandreaN. Elements of the mechanics of solid rigid in Plückerian coordinates, Bucharest: The Publishing House of the Romanian Academy, 2000.
19.
PandreaN. About collisions of two solids with constraints. Rev Romaine SciTechniq Méch Appl2004; 49: 1–6.
20.
Pennestri E, Valentini PP and Vita L. Dynamic analysis of intermittent-motion mechanisms through the combined use of gauss principle and logical functions. In: IUTAM symposium on multiscale problems in multibody system contacts, Stuttgart, February 2006, pp.195–204.
21.
PfeifferF. On impact with friction. Appl Math Comput2010; 217: 1184–1192.
22.
StănescuN-DMunteanuLChiroiuVet al.Dynamical systems. Theory and applications, Bucharest: The Publishing House of the Romanian Academy, 2007.
23.
StrongeJW. Rigid body collision with friction. Proc Roy Soc A1990; 431: 169–181.
24.
StrongeJW. Impact mechanics, Cambridge: Cambridge University Press, 2000.
25.
TavakoliAGharibMHurmuzluY. Collision of two mass baton with massive external surfaces. ASME J Appl Mech2012; 79: 051019 1–8.
26.
Voinea R and Pandrea N. Contribution to a general mathematical theory of kinematic linkages. In: Proceedings of IFTOMM international symposium on linkages and computer design method B, Bucharest, 1973, pp.522–534.
