Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны

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Date:1953
Main Author: Ишлинский, А. Ю.
Format: Article
Language:Russian
Published: Institute of Mathematics, NAS of Ukraine 1953
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/7751
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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author Ишлинский, А. Ю.
Ишлинский, А. Ю.
author_facet Ишлинский, А. Ю.
Ишлинский, А. Ю.
author_sort Ишлинский, А. Ю.
baseUrl_str https://umj.imath.kiev.ua/index.php/umj/oai
collection OJS
datestamp_date 2023-08-15T10:11:31Z
description -
first_indexed 2026-03-24T03:33:30Z
format Article
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OTHOCHTeJibHOe YJJ:JIIIHCI-IHC BCpXI-!CfO 3JICMCHT3 KaHaTa. HarrpoTHB, rrpu HailfaTbmaHHH KaHaTa na KOJieco ecTeCTBei-mo ClfHTaTb ¢YHKU.HIO l ( t) HeH3BCCTHoi1. CooTHOillCHHe ( 15) CB5I3biBaeT B 3TOM cJiyqae I1pOH3BOJJ:HYI-O 3TOH cpymm:rm C OTHOCHTE' JlhHbll\1 y,JJ:JII-UICIIHCM 3JICM-CHTa Ka­ naTa, rrpuxo,n;Hmero B .coiTpHKOCHOBer-me c o6o,n;oM IWJreca. BITpotJeM, H3-3a MaJIOCTII B CJ!HlfHHbl ,n;ecpOplVIall,HH ( 16) flO cpa131ICHHIO C C,UHHllll,CH MO)KHO rrpHHHTb, 'ITO C 60./lblllOi-i TOlfHOCTb!O CrrpaBCJJ;JIHBO p aBCHCTBO dl dt = -v. (17) YMHO)JmM, KaK u paHee, ITpanyJO u .'leByio tJaCTH ,n;ucpcpepeHll,HaJibHOro ypaBI-!CHHH (1 0) Ha nep eMCIIHY!O X H IIpOHI!TerpHpye~I IIX B ITpe,Ue.'laX OT x = 0 ,n;o x = I; ITOJIY'lHi\1 I f o2u(x, Q x at2 0 t) / 2 d~ g au (l, t) / 2 dx-n- - =El --- - - - Eu (l t)- og - ' 2 dt~ ox ' ' 2 . 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Opo,n;IIcpcpepeHU:HpyeM ITo BpeMe Hn o6e traCTH paBeHCTBa {13); Y'IIITbi­ BaH BHOBb, trTO I =l ( t), HMeeM () 2u (l, t) dl asu (r. f) ~~ dv - Jx ot dt + oi~ df~ df ' (22) 373 OTKy,n:a MmKHO HeMe,n:Jreuno orrpe,n:eJIHTb BTopy10 rrpoH3BO,n:uyJO cl>YHKUHH Ht) H llO)J,CTaBHTb ee Bb!paJKe~me B COOHIOWeime (21). B pe3yJibTaTe IIOJIYlJHM CJie,n:yiOIUee OCHOBHOe HI!Terpo-)J,HcpcpepeHUH3JibHOe COOTIIOWCIJHe: ( 1 ) iJSu (/, t) ( 1 ) dl iJ 2u (!, t) m + 2 qFl l-----at2- + m + 2 (!Fl l dt iJx dt - l f iPu (x t) -QF (l-x) iJt2' dx+EFu(l,t)= 0 ( 1 ) dv ( 1 ) = m + 2 QFl l dt + m + ~r (!Fl lg, (23) B KOTOpOM OKpy)JUiaH CKOpOCTb KOJieC a V H cj)yHKUHH f (t) CB5133Hbl paBeH­ CTBOM ( 17) HJIH, B 6o.1ee TOlJHOH nocTaiiOBKe, paneHCTBOM ( 15). CooTHO­ w euue (23) l\IO)KeT 6biTb HCnOJib30Baiio )J,JIH cocTaBJiermH rrpH6J!'H)KeHHbiX ypaBHCIIHH KOJIC03HHH rpy3a !Ia I<aHaTe n ep e MCI-11-IOH )J,JIHHbl. TaK, rrpe,n:rroJiaraH, I<aK H Bbiwe, lJTO ,u:(x, t) = XqJ(t), IIpHXO)J,HM · IIOCJie OlJCB H)J,HbiX rrpeo6pa30B31111H K JIIUieHHOMY )J,HcpcpepeHUH­ aJibHOMY ypaBHCHHIO OTHOCHTCJibHO ci>YHKUHH <p (f) (m + }QFL) i~Jj + (m + ~ (!Fl) ~~ ~1 + EFrp = ( 1 ) dv ( 1 ) = m + 2 qFl di + m + 2 QFI g. (24) YpaBHCIIHe (7) Mmimo paccMaTpHBaTb KaK qacTHbiH CJiylJali ypaBHe­ HHH (24) IIpH f = const H, CJie)J,OBaTeJibHO, B CHJIY paBCHCTBa ( 17) HJIH (15)- rrpn v = 0. DpanaH liaCTh ypam-remm (24) o6ycJIOBJIHBae T npn .9TOM cpe.~nee y,n:JIHHCHHe KaHaTa no,n: ,n:eiiCTBHeM co6cTBeHHoro neca. B ,n:pyroM qacTHOM cJiyqae, ecJm npeHe6pelJb co6cTI3e iiiiOH Maccoi1 Ka­ HaTa, T. e. IIOJ!O)!UiTb B ypaBHCHHH (24) Q = 0, npHXOJLH l\ l K ypaB!I CHHIO, KOTOpoe HCC.lC)J,OBcW H. n. HepoHOB. DpueMaMH, auaJiorHlJHbiMH BhllliC H3JJO)KCHHhiM, MOJIOIO noJiylJaTb HH­ Terpo-,n:mpcpepeuunaJrhHbie COOTHOWCIIHH H npH6JJH)KCHHblC ypaBIICHHH .~JI51 I{aJ-IaTOB rrepeMeimoii )J,JUII-Ibi c yl!eTo~r neconepwem-roi! ynpyroCTH. J11-1TEPATYPA H . n. He p 0 H 0 Il, Onpe,ll.eJielliie narrpmKennii Il ITOJJ:'LCMIIb!X Kawnax, Tpy,ll.bl COIJCIJ.(a­ HIIH no rnaxTHhiM HO).('heM HhiM r<arraTa\·t, Yi3J.(·uo AI-I CCCP, EJt-1'. TioJiy•reHa 16 MaH 1953 r. I< neB. 0370 0371 0372 0373 0374
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institution Ukrains’kyi Matematychnyi Zhurnal
keywords_txt_mv keywords
language rus
last_indexed 2026-03-24T03:33:30Z
publishDate 1953
publisher Institute of Mathematics, NAS of Ukraine
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spelling umjimathkievua-article-77512023-08-15T10:11:31Z Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны Ишлинский, А. Ю. Ишлинский, А. Ю. - Institute of Mathematics, NAS of Ukraine 1953-11-09 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7751 Ukrains’kyi Matematychnyi Zhurnal; Vol. 5 No. 4 (1953); 370-374 Український математичний журнал; Том 5 № 4 (1953); 370-374 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7751/9439 Copyright (c) 1953 А. Ю. Ишлинский
spellingShingle Ишлинский, А. Ю.
Ишлинский, А. Ю.
Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны
title Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны
title_alt Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны
title_full Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны
title_fullStr Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны
title_full_unstemmed Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны
title_short Об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны
title_sort об одном интегро-дифференциальном соотношении в теории упругой нити (каната) переменной длинны
url https://umj.imath.kiev.ua/index.php/umj/article/view/7751
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