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.
