Vol.2, No 10, 2000 pp. 1165-1176
UDC 531.53+534.01(045)
ASYMPTOTIC APPROACHES TO ANALYSIS
OF STRONGLY NON-LINEAR AND NON-SMOOTH SYSTEMS
J. Awrejcewicz
Technical University of Łódź, Division of Automatics and Biomechanics
1/15 Stefanowski St., 90-924 Łódź, Poland (fax: +(4842) 6312225)
E-mail: awrejcew@ck-sg.p.lodz.pl

Abstract. Three important problems of mechanics are addressed. The first corresponds to analytical prediction of a suitable choice of a delay loop parameters in order to control a transitional (perturbed) behaviour of a periodic vibro-impact process modelled by one degree-of-freedom system. The second presents an application of the Melnikov's method to stick-slip chaos prediction in periodically driven self-excited oscillator. The third one illustrates an application of a so called "small ? method" to analysis of strong non-linear oscillations using example of a mathematical pendulum.

ASIMPTOTSKI PRISTUPI ANALIZI
STROGO NELINEARNIH SISTEMA I NEGLATKIH SISTEMA
Rad se odnosi na tri važna problema mehanike. Prvi odgovara analitičkom predviđanju odgovarajućeg izbora parametara kola kašnjenja da bi se upravljalo prelaznim (poremećenim) ponašanjem periodičnog procesa vibro-sudara modeliranog sistemom sa jednim stepenom slobode. Drugi predstavlja primenu Melnikov-ljeve metode na stick-slip predikciju haosa u periodično pobuđenom samopobudnom oscilatoru. Treći ilustruje primenu takozvanog "malog ? metoda" na analizu strogo nelinearnih oscilacija primenom primera matematičkog klatna.