6533b873fe1ef96bd12d4af1
RESEARCH PRODUCT
Theory of Differential Inclusions and Its Application in Mechanics
Gennady A. LeonovGennady A. LeonovNikolay KuznetsovNikolay KuznetsovM. A. Kiselevasubject
Lyapunov function0209 industrial biotechnologyWork (thermodynamics)Mathematical modelDifferential equationMathematical analysis02 engineering and technologyDiscontinuous systems01 natural sciencessymbols.namesake020901 industrial engineering & automationDifferential inclusion0103 physical sciencesCoulombsymbols010301 acousticsFriction torqueMathematicsdescription
The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work, three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load chande is studied. Analytical methods of investigation of systems with such asymmetrical friction, based on the use of Lyapunov functions, are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-09-30 |