Peter Beda | Budapest University of Technology and Economics (original) (raw)

Papers by Peter Beda

AIP Conference Proceedings, 2001

ABSTRACT In the paper we concentrate on the attitude dynamics of a dumbbell satellite on an equat... more ABSTRACT In the paper we concentrate on the attitude dynamics of a dumbbell satellite on an equatorial low Earth orbit. This problem is originated by the application of tethered satellite systems formed by the space shuttle and a tethered subsatellite. These systems are widely studied by NASA and ESA with both theoretical and experimental methods (in the recent years two space shuttle missions performed experiments with tethered satellite systems). The equations of motion of such satellites form a set of highly nonlinear coupled ordinary differential equations, which exhibits very unpleasant behavior when parameters like the length of the dumbbell and the orbit eccentricity is varied. We could detect nonlinear resonances, consecutive period doubling or chaotic oscillations. These are critical phenomena because at deployment or retrieval procedures the length is always changed at each missions. The main aim of this work is to obtain a simple feedback type control between the pitch angle and the length of the dumbbell satellite to get stable behavior in attitude dynamics. By using analytical methods we could derive an approximate equation of motion, which can be used as a model of the “real” system of equations. The approximate equation can be studied by applying nonlinear analysis and bifurcation theory and the conclusions are used as anticipations in building the feedback control. © 2001 American Institute of Physics.

AIP Conference Proceedings, 2006

Bifurcation in the sense of applied mathematics happens when the system is on the boundary of one... more Bifurcation in the sense of applied mathematics happens when the system is on the boundary of one set of equivalent states. Generally a system undergoing bifurcation is in a critical state. Any small change in the parameters may result essentially different behaviors. This phenomenon is called the structural instability and is of great interest in (Lyapunov) stability investigations of engineering problems. In numerical simulations such property may cause several problems. We concentrate on the differences in the qualitative behavior of the solutions for recursive and anticipatory systems generated by the same mechanical model. The results show how the nature of solution depends on the type of bifurcation.

AIP Conference Proceedings, 2002

The stability or stabilization of an inverted pendulum is a textbook example for analytical mecha... more The stability or stabilization of an inverted pendulum is a textbook example for analytical mechanics or control theory because it is a simple and generally used model of several engineering problems. In this paper we study the behavior of an excited inverted pendulum in the post-critical region. A simple feedback control is applied to avoid chaotic oscillations. While our problem is originated by an astronautical device (dumbbell satellite) the controller changes the length of the pendulum as the angular position is varied. We use two approaches in numerical simulation. The one is of recursive nature while the other is an incursive one and we detect that the qualitative picture of the trajectories may be different even for the same parameter values.

The stability of an inverted pendulum is a textbook example of control. The easiest case is to pu... more The stability of an inverted pendulum is a textbook example of control. The easiest case is to put the pendulum on a cart and apply feedback force control on it to keep the upright position stable. This paper compares the no delay case (feed-in-time control: an anticipatory effect) and the delay differential equation approach. Then we study both continuous and discrete time systems. The main aim of the work is to investigate the behaviour of such systems at the stability boundaries by using numerical simulation. The principal points of interest are how continuous time systems differ from discrete time system at a bifurcation point and how time delay or an anticipatory feed-in-time control acts on its behaviour. Other exciting questions are how sampling delay can be taken into consideration and is bifurcation a robust phenomenon.

Nonlinear Analysis: Theory, Methods & Applications, 1997

Materials Science Forum, 2010

There are several self-sustained oscillatory phenomena observed at plastic deformation of metals.... more There are several self-sustained oscillatory phenomena observed at plastic deformation of metals. One of them happens at the beginning of plastic behavior and leads to appearance of the famous Lüders-Hartmann bands. However, it can also be found self-sustained oscillations well beyond the yield stress like Portevin and Le Chatelier did in the early 20th century. This paper presents a simple model of that by using continuum approach and the theory of dynamical systems.

PAMM, 2009

In a phenomenon called the Portevin‐Le Chatelier (PLC) effect negative rate dependence is coupled... more In a phenomenon called the Portevin‐Le Chatelier (PLC) effect negative rate dependence is coupled with the appearance of a self‐sustained oscillatory behavior in solid bodies. When PLC is treated as a type of dynamic material instability, the tools of the theory of dynamical system can be applied. The results of such investigation lead to an interpretation of PLC as a flutter type of loss of stability. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

International Journal of Bifurcation and Chaos, 1995

This letter investigates the effect of the length of an Earth orbiting dumbbell system on the num... more This letter investigates the effect of the length of an Earth orbiting dumbbell system on the number and the Lyapunov stability of its stationary motions. This effect appears when a weak aerodynamical drag is taken into consideration and being important for low orbit satellites. The equation of motion is obtained as a Lagrange equation. Using analytical methods a critical length can be found causing essential changes in the structure of the set of stationary positions and in the stability properties, too. For longer systems the number of stationary positions is four, for shorter ones it is two. In the critical case the other two positions come together and disappear in a saddle-node bifurcation. The numerical values of the bifurcation point and of the critical length are also presented in a case described in the literature.

Dynamics and Stability of Systems, 1992

... Page 10. 228 PB BEDA, A. STEINDL AND H. TROGER where k = EJ/GJT is used. ... which is the coe... more ... Page 10. 228 PB BEDA, A. STEINDL AND H. TROGER where k = EJ/GJT is used. ... which is the coefficient of q: in (47), we obtain two differential equations of the form with the boundary conditions 3i(0)=3i(0) = 3i(0)=3i(l) = 0, i = 1,2. The solution of (48) is given by (Frank and Mises, 1961) ...

Vehicle System Dynamics

Vehicle safety is an important field of today's engineering practice and the scientific resea... more Vehicle safety is an important field of today's engineering practice and the scientific research as well. One of the basics of the modern vehicle system dynamics control systems is braking or drivi...

Soviet Applied Mechanics, 1991

International Journal of Mechanical Sciences, 2000

A nemlokális testek anyagtörvényeinek a szakcikkekben 8-féle felépítési módját találtuk. A lehető... more A nemlokális testek anyagtörvényeinek a szakcikkekben 8-féle felépítési módját találtuk. A lehetőségek viszonylag nagy száma miatt arra következtettünk, hogy a nemlokális testek anyagtörvényének nincs elfogadott alakja. A felvetett 8 felépítési módból a kutatás során kettőt vizsgáltunk részletesen, mégpedig a Mindlin-féle anyag esetét és a hullámdinamikai anyagtörvény meghatározási módot. A kapott eredmények arra vezetnek, hogy a feszültség tenzor egy funkcionál Lagrange deriváltja. Bevezettük a feltételes Lagrange deriváltat, amely biztosítja a hullámdinamikai elmélet által megkövetelt gyorsuláshullám létezését. Az ilyen Lagrange derivált a nemlokális test általánosabb alakjat értelmezi. Az anyagi instabilitás kutatása a dinamikai rendszerek elméletében kidolgozott módszerek alkalmazását teszi lehetővé. A feladatban ilyen módon a Ljapunov-féle vizsgálati módszerek felhasználásával az anyagtörvény újabb lehetséges változói jelennek meg azonfelül, hogy tisztázható a bifurkációelmélet...

International Journal of Structural Stability and Dynamics

Xi Magyar Mechanikai Konferencia, Feb 20, 2011