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PONAŠANJE BRODA NA TALASIMA____________________________1. KOMPONENTE LJULJANJA BRODA I POLAZNE JEDNAČINEŠest generalisanih koordinata,šest “ljuljanja”, suBrod na talasima je kruto telo koje vršiopšte kretanje...šest stepeni slobode...Uvodimo dva koordinatna sistemasopstveni sistem x, y, z (sistem vezan zabrod) sa poćetkom u G,i inercijalni sistem ξ, η, ζ, sa početkom u O .Kada brod pliva u ravnoteži, bez trima inagiba, sistemi se poklapaju...zamisli...ξ G - zaletanje (surge),η G - zanošenje (sway),ζ G – poniranje (heave),φ - valjanje (roll),ψ - posrtanje (pitch),θ - zakretanje (yaw),Koristimo Njutnov zakonm ⋅ a = FB G Ri Zakon o promeni momentakoličine kretanja (za težište G)dL G= MGdtPREDAVANJA 2009. 7
PONAŠANJE BRODA NA TALASIMA____________________________Projektovanjem Njutnovogzakona na tri inercijalneose slediD ⋅ ξ =GF ξD ⋅ ηG= F ηD ⋅ ζ = F −D⋅gGζJ ϕ + ( J −J ) ψθ − J ( θ + ϕψ) = Mx z y xz xJ ψ + ( J − J ) ϕθ+ J ( ϕ 2 − θ2 ) = My x z xz yJ θ + ( J −J ) ψϕ −J ( ϕ− ψθ )= Mz y x xz zOsa y – glavna osa inercije... J = J = 0,J = J = 0xy yx yz zyPri čemu je FR= W + F V+ vetar W = m ⋅gVBmB= D F = F F F FV( ξ,η,ζ )Projektovanjem Zakonao promeni momentakoličine kretanja na trisopstvene ose, slediJ xz = J zx postoji...ali je mali u odnosu na aksijalne momente inercije, J xz « J x ,J y ,J zPretpostavljamo, takođe, da su kretanja mala...φ(t), ψ(t), θ(t) « 1Pretpostavka dobra za posrtanje i zakretanje, ali sumljiva zavaljanje...J ϕ =MxxJ yψ = MJ θ = MzzyJednačine ne deluju “opasno”... aliPREDAVANJA 2009. 8
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