Double pendulum colliding with a rough obstacle.
Ładowanie...
Data
2015
Tytuł czasopisma
ISSN czasopisma
Tytuł tomu
Wydawca
Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.
Abstrakt
The 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.
Opis
Słowa kluczowe
systems theory - conference, dynamical systems - conference, mechatronics - conference, teoria systemów, systemy dynamiczne, mechatronika, podwójne wahadlo
Cytowanie
Dynamical systems : mechatronics and life sciences ; s. 483-492