Brahistohrono opšte kretanje krutog tela
Brachistochronic rigid body general motion
Abstract
Razmatra se minimizacija vremena kretanja krutog tela uz neizmenjenu vrednost mehaničke energije. Za generalisane koordinate uzete su koordinate centra masa i Ojlerovi uglovi, čije su vrednosti zadate na početku i kraju intervala kretanja. Zadatak je rešen primenom Pontrjaginovog principa maksimuma. Numeričko rešenje dvotačkastog graničnog problema dobijeno je metodom konačnih razlika za sisteme običnih diferencijalnih jednačina. .
The time interval minimization of rigid body motion with constant mechanical energy has been considered in this paper. Generalized coordinates are Cartesian's coordinates of mass center and the Euler's angles, which are specified at the initial and the final position. The problem has been solved by the application of the Pontryagin's principle. Finite difference method has been applied in order to obtain the solution of the two-point boundary value problem. .
Keywords:
rigid body / Pontryagin's principle / finite difference / brachistochronic motionSource:
FME Transactions, 2008, 36, 3, 109-112Publisher:
- Univerzitet u Beogradu - Mašinski fakultet, Beograd
Funding / projects:
- Razvoj mašina visokih performansi i metoda za identifikaciju njihovog odziva na unutrašnje i spoljašnje poremećaje (RS-MESTD-MPN2006-2010-14052)
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Institution/Community
Mašinski fakultetTY - JOUR AU - Obradović, Aleksandar AU - Mladenović, Nikola AU - Marković, Saša PY - 2008 UR - https://machinery.mas.bg.ac.rs/handle/123456789/797 AB - Razmatra se minimizacija vremena kretanja krutog tela uz neizmenjenu vrednost mehaničke energije. Za generalisane koordinate uzete su koordinate centra masa i Ojlerovi uglovi, čije su vrednosti zadate na početku i kraju intervala kretanja. Zadatak je rešen primenom Pontrjaginovog principa maksimuma. Numeričko rešenje dvotačkastog graničnog problema dobijeno je metodom konačnih razlika za sisteme običnih diferencijalnih jednačina. . AB - The time interval minimization of rigid body motion with constant mechanical energy has been considered in this paper. Generalized coordinates are Cartesian's coordinates of mass center and the Euler's angles, which are specified at the initial and the final position. The problem has been solved by the application of the Pontryagin's principle. Finite difference method has been applied in order to obtain the solution of the two-point boundary value problem. . PB - Univerzitet u Beogradu - Mašinski fakultet, Beograd T2 - FME Transactions T1 - Brahistohrono opšte kretanje krutog tela T1 - Brachistochronic rigid body general motion EP - 112 IS - 3 SP - 109 VL - 36 UR - https://hdl.handle.net/21.15107/rcub_machinery_797 ER -
@article{ author = "Obradović, Aleksandar and Mladenović, Nikola and Marković, Saša", year = "2008", abstract = "Razmatra se minimizacija vremena kretanja krutog tela uz neizmenjenu vrednost mehaničke energije. Za generalisane koordinate uzete su koordinate centra masa i Ojlerovi uglovi, čije su vrednosti zadate na početku i kraju intervala kretanja. Zadatak je rešen primenom Pontrjaginovog principa maksimuma. Numeričko rešenje dvotačkastog graničnog problema dobijeno je metodom konačnih razlika za sisteme običnih diferencijalnih jednačina. ., The time interval minimization of rigid body motion with constant mechanical energy has been considered in this paper. Generalized coordinates are Cartesian's coordinates of mass center and the Euler's angles, which are specified at the initial and the final position. The problem has been solved by the application of the Pontryagin's principle. Finite difference method has been applied in order to obtain the solution of the two-point boundary value problem. .", publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd", journal = "FME Transactions", title = "Brahistohrono opšte kretanje krutog tela, Brachistochronic rigid body general motion", pages = "112-109", number = "3", volume = "36", url = "https://hdl.handle.net/21.15107/rcub_machinery_797" }
Obradović, A., Mladenović, N.,& Marković, S.. (2008). Brahistohrono opšte kretanje krutog tela. in FME Transactions Univerzitet u Beogradu - Mašinski fakultet, Beograd., 36(3), 109-112. https://hdl.handle.net/21.15107/rcub_machinery_797
Obradović A, Mladenović N, Marković S. Brahistohrono opšte kretanje krutog tela. in FME Transactions. 2008;36(3):109-112. https://hdl.handle.net/21.15107/rcub_machinery_797 .
Obradović, Aleksandar, Mladenović, Nikola, Marković, Saša, "Brahistohrono opšte kretanje krutog tela" in FME Transactions, 36, no. 3 (2008):109-112, https://hdl.handle.net/21.15107/rcub_machinery_797 .