Vol.2, No 10, 2000 pp. 1191-1202
UDC 531.231.531.5:517.925.4(045)

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QUADRATIC CONSERVATION LAWS
FOR ONE-DEGREE-OF-FREEDOM MASS VARIABLE OSCILLATORS
Livija Cvetićanin
Faculty of Engineering, 21000 Novi Sad, Trg D. Obradovica 6, Yugoslavia

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Abstract. In this paper the one-degree-of-freedom mass variable oscillators are considered. The mass variation is a function of time. Due to mass variation the reactive force acts. The motion of this system is described with a second order differential equation with time variable parameters. To find the closed form solution of the equation is impossible. In this paper the conservation laws of the systems are considered. The system has a Lagrangian. To form the invariants of the system the Noether's approach is applied. It is applied for determining the conservation laws of the rheo-linear, pure-cubic oscillator and a pendulum with variable mass and length.

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KVADRATNI ZAKONI ODRŽANJA ZA OSCILATORE PROMENLJIVE MASE SA JEDNIM STEPENOM SLOBODE U ovom radu se razmatraju oscilatori promenljive mase sa jednim stepenom slobode. Promena mase je funkcija vremena. Usled promene mase se javlja reaktivna sila. Kretanje ovog sistema je opisano diferencijalnom jednačinom drugog reda sa vremenski promenljivim parametrima. Nemoguće je naći rešenje ove jednačine u zatvorenom obliku. U ovom radu razmatraju se zakoni održanja sistema. Za formiranje invarijanti sistema primenjen je Noether-in pristup. On je primenjen za određivanje zakona održanja reo-linearnog, čisto kubnog oscilatora i klatna pro-menljive mase i dužine.