Double pendulum colliding with a rough obstacle.

dc.contributor.authorSypniewska-Kamińska, Grażyna
dc.contributor.authorStarosta, Roman
dc.contributor.authorAwrejcewicz, Jan
dc.description.abstractThe externally excited and damped vibrations of the double pendulum in the vertical plane are considered. The pendulum can collide with a rough obstacle many times during its motion. The pendulum is modeled as a piecewise smooth system. The differential equations govern the motion of the system in the relatively long time between the collisions. When a contact with the obstacle occurs, the pendulum exhibits a discontinuous behaviour. The velocities of both parts of the pendulum and the reaction forces are changing stepwise. An important element of the solving algorithm is aimed on the continuous tracking of the position of the pendulum in order to detect the collision with the unilateral constraints and to determine the state vector of the pendulum at the impact time instant. A single collision is described by the Euler’s laws of motion in the integral form. The equations are supplemented by the Poisson's hypothesis and Coulomb’s law of friction. The friction law is formulated for the instantaneous values of the reaction forces. The values of their impulses depend on the existence of a slip between the contacting bodies. Furthermore, during the collision the dynamic behaviour may change. Therefore the Coulomb law cannot be generalized for the linear impulses of the forces in a simple way. We have applied the Routh method in order to solve the problem. The method has a simple geometrical interpretation in the impulse space.en_EN
dc.identifier.citationDynamical systems : mechatronics and life sciences ; s. 483-492en_EN
dc.publisherPolitechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.pl_PL
dc.relation.ispartofseriesDynamical systems : mechatronics and life sciences, 2015en_EN
dc.subjectsystems theory - conferenceen_EN
dc.subjectdynamical systems - conferenceen_EN
dc.subjectmechatronics - conferenceen_EN
dc.subjectteoria systemówpl_PL
dc.subjectsystemy dynamicznepl_PL
dc.subjectpodwójne wahadlopl_PL
dc.titleDouble pendulum colliding with a rough obstacle.en_EN


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