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PONAŠANJE BRODA NA TALASIMA____________________________2.4. Spregnuto poniranje i posrtanje brodaPretpostavljamo da brod istovremeno ponire iposrćeKretanje sa 2 stepena slobode ζ (), t ψ G ()tPretpostavljamo da nema zaletanja ξ G() t = 0Pretpostavljamo (za sada) i da nema napredovanjabroda, v o = 0G se kreće vertikalno, po osi ζ ...a brod vrši ravansko kretanja...Diferencijalne jednačine kretanja slede izD ⋅ ζG= Fζ−D⋅gJ ψ = MyyKretanje pojedinih tačaka broda jerazličito...Delimo brod na elemente (trake)dužine dxna svaku traku deluje elementarnasila dfUkupnu silu dobijamo integracijom...Treba uočiti (dokazati)• da se sve trake, kreću približnovertikano...• da je strujanje oko trakaravansko, u ravni ogovarajućegrebra• da su sile df približno vertikalneTo je posledica malog ugla ψ, ivitkosti forme uobičajenih brodova...PREDAVANJA 2009. 19
PONAŠANJE BRODA NA TALASIMA____________________________Posmatrajmo brzinu proizvoljne tačkebroda ATačke broda se kreču približnovertikalno....VaživAζ =f( x)ASve tačke jedne trake imaju(približno) istu brzinuv = v +vGA G AGv = ζ , v = r ⋅ψG G A Avζ= ζ ≈ ζ − rψcosα = ζ −xψA A G A A G Avξ= ξ ≈ rψsinα = z ψA A A A ATrake se kreću vertikalno, brzinom ζ ≈ ζ −xψ A G APomeranje trake je∫ζ = v dt ≈ζ −x⋅ψA AζG AUbrzanje trake jeVaživAζ vAξdvAζaA ζ= ζA= ≈ ζG −xA⋅ ψdtPREDAVANJA 2009. 20
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