Čvor
Čvor je splet ili zadevljanje koje nastaje kada se delovi nečega savitljivog (konca, užeta, žice i sl.)[1] čvrsto vežu ili zamrse na jednom mestu.[2] Čvorovi se mogu koristiti u ozbiljne ili u dekorativne svrhe. Kada oštećeno uže pukne, vezuje se u čvor radi daljeg održavanja svoje funkcije. Ponekad se uže kvasi kako bi se dodatno ojačalo i čvor bio snažniji. Čvorovi se takođe koriste i kod transporta. Razne vrste kamiona, traktora i drugih prevoznih sredstava koriste čvor kako bi svoje vozilo povezali sa prikolicom.
Savijanje pričvršćuje dva kraja užeta jedan za drugi; čvor petlje je svaki čvor koji stvara petlju; a spajanje označava svaki višelančani čvor, uključujući krivine i petlje.[3] Čvor se takođe može odnositi, u najstrožem smislu, na graničnik ili dugme na kraju užeta kako bi se sprečilo da taj kraj isklizne kroz otvor ili oko.[4] Čvorovi su od davnina izazivali interesovanje za njihovu praktičnu upotrebu, kao i za njihovu topološku zamršenost, proučavanu u oblasti matematike poznatoj kao teorija čvorova.
Svojstva[uredi | uredi izvor]
Jačina[uredi | uredi izvor]
Čvorovi slabe konopac u kome su napravljeni.[5] Kada je konopac sa čvorom napet do tačke kidanja, skoro uvek se prekida u čvoru ili blizu njega, osim ako je neispravan ili oštećen na drugom mestu. Sile savijanja, gnječenja i habanja koje drže čvor na mestu takođe neravnomerno naprežu vlakna užeta i na kraju dovode do smanjenja snage. Tačni mehanizmi koji uzrokuju slabljenje i neuspeh su složeni i predmet su kontinuiranog proučavanja. Posebna vlakna koja pokazuju razlike u boji kao odgovor na naprezanje se razvijaju i koriste za proučavanje stresa u vezi sa tipovima čvorova.[6][7]
Relativna čvrstoća čvora, takođe nazvana efikasnost čvora, je snaga kidanja užeta sa čvorovima u proporciji sa snagom kidanja užeta bez čvora. Određivanje precizne vrednosti za određeni čvor je teško jer mnogi faktori mogu uticati na test efikasnosti čvora: vrsta vlakana, stil užeta, veličina užeta, da li je mokro ili suvo, kako je čvor obučen pre naprezanja, koliko brzo se napreže, da li se čvor više puta opterećuje i tako dalje. Efikasnost uobičajenih čvorova kreće se između 40 i 80% prvobitne snage užeta.[8] [9]
U većini situacija formiranje petlji i krivina sa konvencionalnim čvorovima je daleko praktičnije od upotrebe spojeva užeta, iako potonji mogu održati skoro punu snagu užeta. Razboriti korisnici dozvoljavaju veliku sigurnosnu marginu u čvrstoći užeta odabranog za zadatak zbog slabljenja efekata čvorova, starenja, oštećenja, udarnog opterećenja itd. Granica radnog opterećenja užeta je generalno određena sa značajnim faktorom sigurnosti, do 15:1 za kritične aplikacije.[10]
Teorija čvorova[uredi | uredi izvor]
Teorija čvorova je grana topologije. Bavi se matematičkom analizom čvorova, njihovom strukturom i svojstvima, kao i odnosima između različitih čvorova. U topologiji, čvor je figura koja se sastoji od jedne petlje sa bilo kojim brojem ukrštenih ili čvorovanih elemenata: zatvorena kriva u prostoru koja se može pomerati sve dok njene niti nikada ne prolaze jedna kroz drugu. Kao zatvorena petlja, matematički čvor nema odgovarajuće krajeve i ne može se poništiti ili odvezati; međutim, svaki fizički čvor u parčetu kanapa može se smatrati matematičkim čvorom spajanjem dva kraja. Konfiguracija od nekoliko čvorova koji se obavijaju jedan oko drugog naziva se veza. Za klasifikaciju i razlikovanje čvorova i karika koriste se različite matematičke tehnike. Na primer, Aleksandrov polinom povezuje određene brojeve sa bilo kojim datim čvorom; ovi brojevi su različiti za trolisni čvor, čvor sa osmom i nečvor (jednostavnu petlju), pokazujući da se jedan ne može pomeriti u drugi (bez da niti prolaze jedna kroz drugu).[11]
Fizička teorija frikcionih čvorova[uredi | uredi izvor]
Jednostavnu matematičku teoriju zastoja je predložio Bejman,[12] a proširili Madoks i Keler.[13] On daje predviđanja koja su približno tačna kada se testiraju empirijski.[14] Nijedna slično uspešna teorija nije razvijena generalno za čvorove.
Reference[uredi | uredi izvor]
- ^ Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, str. 12, „"The word knot has three distinct meanings in common use. In the broadest sense it applies to all complications in cordage, except accidental ones, such as snarls and kinks, and complications adapted for storage, such as coils, hanks, skeins, balls, etc."”
- ^ Rečnik srpskoga jezika. Novi Sad: Matica srpska. 2011. str. 1475.
- ^ Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, str. 12
- ^ Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, str. 12, „"In its second sense it does not include bends, hitches, splices, and sinnets, and in its third and narrowest sense the term applies only to a knob tied in a rope to prevent unreeving, to provide a handhold, or (in small material only) to prevent fraying."”
- ^ Richards, Dave (2005). „Knot Break Strength vs Rope Break Strength”. Nylon Highway. Vertical Section of the National Speleological Society (50). Pristupljeno 2010-10-11.
- ^ Greenfieldboyce, Nell (2. 1. 2020). „A Knotty Problem Solved”. All Things Considered. Pristupljeno 3. 1. 2020.
- ^ Patil, Vishal P.; Sandt, Joseph D.; Kolle, Mathias; Dunkel, Jörn (3. 1. 2020). „Topological Mechanics of Knots and Tangles”. Science. 367 (6473): 71—75. Bibcode:2020Sci...367...71P. PMID 31896713. S2CID 209677605. doi:10.1126/science.aaz0135
.
- ^ Warner, Charles (1996), „Studies on the Behaviour of Knots”, Ur.: Turner, J.C.; van de Griend, P., History and Science of Knots, K&E Series on Knots and Everything, 11, Singapore: World Scientific Publishing, str. 181—203, ISBN 978-981-02-2469-1
- ^ Šimon; Dekýš, V.; Palček, P. (2020). „Revision of Commonly Used Loop Knots Efficiencies”. Acta Physica Polonica A. 138 (3): 404—420. doi:10.12693/APhysPolA.138.404 .
- ^ „Knot & Rope Safety”. Animated Knots by Grog. 2010. Arhivirano iz originala 7. 4. 2015. g. Pristupljeno 2010-09-14.. "Knot & Rope Safety", AnimatedKnots.com. Accessed April 2016.
- ^ Nakanishi, Yasutaka; Okada, Yuki (2012). „Differences of Alexander polynomials for knots caused by a single crossing change”. Topology and Its Applications. 159 (4): 1016—1025. doi:10.1016/j.topol.2011.11.023 .
- ^ Bayman, "Theory of hitches," Am J Phys, 45 (1977) 185
- ^ Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185–1200.
- ^ „The physics of knots”. www.lightandmatter.com.
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Spoljašnje veze[uredi | uredi izvor]
- Knots na sajtu Curlie
- KnotInfo: Table of Knot Invariants and Knot Theory Resources
- The Knot Atlas — detailed info on individual knots in knot tables
- KnotPlot — software to investigate geometric properties of knots
- Knotscape — software to create images of knots
- Knoutilus Arhivirano na sajtu Wayback Machine (27. jun 2020) — online database and image generator of knots
- KnotData.html — Wolfram Mathematica function for investigating knots
- Regina Arhivirano na sajtu Wayback Machine (11. avgust 2022) — software for low-dimensional topology with native support for knots and links. Tables of prime knots with up to 19 crossings
- Movie Arhivirano na sajtu Wayback Machine (24. septembar 2015) of a modern recreation of Tait's smoke ring experiment
- History of knot theory (on the home page of Andrew Ranicki)
