Analiza kretanja i stabilnosti holonomnog mehaničkog sistema u proizvoljnom polju sila
Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field
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.
Keywords:
Stability of motion / Lagrange's equation / Coulomb friction Hamiltonian function / Applied mechanicsSource:
FME Transactions, 2021, 49, 1, 195-205Publisher:
- Univerzitet u Beogradu - Mašinski fakultet, Beograd
Funding / projects:
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
- Ministry of Science, Technological Development and Innovation of the Republic of Serbia, institutional funding - 200105 (University of Belgrade, Faculty of Mechanical Engineering) (RS-MESTD-inst-2020-200105)
DOI: 10.5937/fme2101195V
ISSN: 1451-2092
WoS: 000595729200022
Scopus: 2-s2.0-85113196523
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Vesović, Mitra AU - Petrović, Goran R. AU - Radulović, Radoslav PY - 2021 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3579 AB - 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. AB - 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. PB - Univerzitet u Beogradu - Mašinski fakultet, Beograd T2 - FME Transactions T1 - Analiza kretanja i stabilnosti holonomnog mehaničkog sistema u proizvoljnom polju sila T1 - Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field EP - 205 IS - 1 SP - 195 VL - 49 DO - 10.5937/fme2101195V ER -
@article{ author = "Vesović, Mitra and Petrović, Goran R. and Radulović, Radoslav", year = "2021", 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.", publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd", journal = "FME Transactions", title = "Analiza kretanja i stabilnosti holonomnog mehaničkog sistema u proizvoljnom polju sila, Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field", pages = "205-195", number = "1", volume = "49", doi = "10.5937/fme2101195V" }
Vesović, M., Petrović, G. R.,& Radulović, R.. (2021). Analiza kretanja i stabilnosti holonomnog mehaničkog sistema u proizvoljnom polju sila. in FME Transactions Univerzitet u Beogradu - Mašinski fakultet, Beograd., 49(1), 195-205. https://doi.org/10.5937/fme2101195V
Vesović M, Petrović GR, Radulović R. Analiza kretanja i stabilnosti holonomnog mehaničkog sistema u proizvoljnom polju sila. in FME Transactions. 2021;49(1):195-205. doi:10.5937/fme2101195V .
Vesović, Mitra, Petrović, Goran R., Radulović, Radoslav, "Analiza kretanja i stabilnosti holonomnog mehaničkog sistema u proizvoljnom polju sila" in FME Transactions, 49, no. 1 (2021):195-205, https://doi.org/10.5937/fme2101195V . .