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I.-B. Dragna et al.
• the greatest number of collision appears for the first rigid body;
• increasing the index of the rigid body, the diagrams of variation for the position
and velocity maintain a vague harmonic shape, the number of collisions decreases,
and the time for which the rigid body is in continuous contact with one stopper
increases;
• it is possible that at one or more rigid bodies, no collision occurs (the rigid body
3 in our case), that is, those rigid bodies have an oscillatory motion in an interval
between the two corresponding stoppers;
• the number of collisions and the time of continuous contacts depend on the values
of the coefficients of restitution. Increasing the values for coefficient of restitutions, the number of collisions increases, while the time of continuous contact
decreases;
• smaller values for the distances between the stoppers lead to higher numbers of
collisions.
4 Conclusions
In our paper, we consider a mechanical system for which we study its dynamics based
on the possible collisions that may appear between one or many of its components
and some stoppers situated along their directions of motion.
The study highlighted the complexity of the dynamics of such system and the
absence of periodicity of the motion. In fact, it is possible that one rigid may stay
in permanent contact with one of its stoppers, or another rigid may not collide at
any of its own stoppers. The dynamics may become more complex if one considers
nonlinear springs or another excitation (a non-harmonic one). These will be the goals
of our future works.
References
1. J.A. Batlle, Termination condition for three-dimensional inelastic collisions in multibody
systems. Int. J. Impact Eng. 25(7), 615–629 (2001)
2. J.A. Batlle, The sliding velocity flow of rough collisions in multibody systems. ASME J. Appl.
Mech. 63(3), 804–809 (1996)
3. J.A. Batlle, S. Cardona, The jamb (self locking) process in three-dimensional collisions. ASME
J. Appl. Mech. 65(2), 417–423 (1998)
4. R.M. Brach, Friction restitution and energy loss in planar collision. ASME J. Appl. Mech.
51(1), 164–170 (1984)
5. R.M. Brach, Rigid body collision. ASME J. Appl. Mech. 56(1), 133–138 (1989)
6. B. Brogliato, Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with
impacts and friction. Multibody Syst. Dyn. 32, 175–216 (2014)
7. B. Brogliato, Nonsmooth Mechanics, 3rd edn. (Springer, Berlin, 2016)
8. F. Dimentberg, The Theory of Screws and its Applications (Nauka, Moskow, 1978)
9. H.A. Elkaranshawy, Rough collision in three-dimensional rigid multi-body systems. Proc. Inst.
Mech. Eng. Part K J. Multi-body Dyn. 221(4), 541–550 (2007)
I.-B. Dragna et al.
• the greatest number of collision appears for the first rigid body;
• increasing the index of the rigid body, the diagrams of variation for the position
and velocity maintain a vague harmonic shape, the number of collisions decreases,
and the time for which the rigid body is in continuous contact with one stopper
increases;
• it is possible that at one or more rigid bodies, no collision occurs (the rigid body
3 in our case), that is, those rigid bodies have an oscillatory motion in an interval
between the two corresponding stoppers;
• the number of collisions and the time of continuous contacts depend on the values
of the coefficients of restitution. Increasing the values for coefficient of restitutions, the number of collisions increases, while the time of continuous contact
decreases;
• smaller values for the distances between the stoppers lead to higher numbers of
collisions.
4 Conclusions
In our paper, we consider a mechanical system for which we study its dynamics based
on the possible collisions that may appear between one or many of its components
and some stoppers situated along their directions of motion.
The study highlighted the complexity of the dynamics of such system and the
absence of periodicity of the motion. In fact, it is possible that one rigid may stay
in permanent contact with one of its stoppers, or another rigid may not collide at
any of its own stoppers. The dynamics may become more complex if one considers
nonlinear springs or another excitation (a non-harmonic one). These will be the goals
of our future works.
References
1. J.A. Batlle, Termination condition for three-dimensional inelastic collisions in multibody
systems. Int. J. Impact Eng. 25(7), 615–629 (2001)
2. J.A. Batlle, The sliding velocity flow of rough collisions in multibody systems. ASME J. Appl.
Mech. 63(3), 804–809 (1996)
3. J.A. Batlle, S. Cardona, The jamb (self locking) process in three-dimensional collisions. ASME
J. Appl. Mech. 65(2), 417–423 (1998)
4. R.M. Brach, Friction restitution and energy loss in planar collision. ASME J. Appl. Mech.
51(1), 164–170 (1984)
5. R.M. Brach, Rigid body collision. ASME J. Appl. Mech. 56(1), 133–138 (1989)
6. B. Brogliato, Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with
impacts and friction. Multibody Syst. Dyn. 32, 175–216 (2014)
7. B. Brogliato, Nonsmooth Mechanics, 3rd edn. (Springer, Berlin, 2016)
8. F. Dimentberg, The Theory of Screws and its Applications (Nauka, Moskow, 1978)
9. H.A. Elkaranshawy, Rough collision in three-dimensional rigid multi-body systems. Proc. Inst.
Mech. Eng. Part K J. Multi-body Dyn. 221(4), 541–550 (2007)