Open AccessIndetermination versus incompatibility in dynamic systems with dry friction
Author(s) -
Stelian Alaci,
Florina-Carmen Ciornei,
Radu Dumitru Pentiuc,
Mariana-Catalina Ciornei,
Ionut-Cristian Romanu
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1426/1/012011
Subject(s) - dry friction , ball (mathematics) , planar , dynamical systems theory , classical mechanics , equations of motion , dynamical system (definition) , mathematics , motion (physics) , simple (philosophy) , mathematical analysis , physics , computer science , materials science , philosophy , computer graphics (images) , epistemology , quantum mechanics , composite material
The study of the dynamical behavior of a system becomes really complex when friction forces are introduced in calculus since they directly depend on the values of the normal reactions and on the motion of the system, but the motion, at its turn, depends upon the forces from the system. The analysis is more difficult when dry friction, characterized by inequalities, is present between the parts of the system. When inequalities are involved in dynamical equilibrium equations, theoretically simultaneous equilibrium states may occur. In scientific literature there are famous examples supporting this statement. The present paper presents the dynamical study of a simple system, namely a ball obliged to roll in a groove with flat walls. It is proved experimentally that the motion of the ball is a planar one. The dynamical analysis of the system with planar motion leads to an undeterminate system of equations and therefore the spatial approach of the system is required. After writing the equations of the spatial motion of the ball, an incompatible system of equations is obtained.