Analiza kretanja i stabilnosti holonomnog mehaničkog sistema u proizvoljnom polju sila

Abstract

U cilju dobijanja uvida u rad mašine pre njene montaže i proizvodnje, kao i dobijanja dobre analize, ovaj rad predstavlja detaljna rešenja specifičnog problema iz oblasti analitičke mehanike. Pored numeričkih postupaka u radu, izvršen je i pregled teorijskih osnova. Razne vrste analiza su vrlo česte u mašinskom inženjerstvu, zbog mogućnosti aproksimacije složenih mašina. Za predloženi sistem date su Lagranžove jednačine prve vrste, kovarijantne i kontravarijantne jednačine, Hamiltonove jednačine, generalisane koordinate, kao i uvid u Kulonovu silu trenja. Takođe, rešeni su i uslovi statičke ravnoteže uz pomoć numeričkih i grafičkih postupaka - presekom dve krive. Konačno, razmatrana je i stabilnost kretanja poremećenog i neporemećenog kretanja.

In order to give an insight into the work of the machine before the production and assembly and to obtain good analysis, this paper presents detailed solutions to the specific problem occured in the field of analytical mechanics. In addition to numerical procedures in the paper, a review of the theoretical foundations was made.Various types of analysis are very common in mechanical engineering, due to the possibility of an approximation of complex machines. For the proposed system, Lagrange's equations of the first kind, covariant and contravariant equations, Hamiltons equations and the generalized coordinates, as well as insight in Coulumb friction force are provided.Also, the conditions of static equilibrium are solved numerically and using intersection of the two curves. Finally, stability of motion for the disturbed and undisturbed system was investigated.