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PONAŠANJE BRODA NA TALASIMA____________________________Izraze možemo napisati u kompleksnom oblikuζ ′ =TpAe ωoTi( t+ε )Ti( t + + )p T ZZ = Z e ω ε γgde samo realni idelovi ifunkcija imaju svojefizičko značenjeIzlaz svodimo na fazu ulaza...iγ i( t+)Z p TZ = Z e ⋅e ω εoodnosno uvodimo tzv. kompleksnu amplitudu izlazaKompleksna prenosna funkcija, prematome, transformiše ulaz u izlazZ = P ⋅ζ ′ZNjen modul – realna funkcija P Z ,transformiše amplitudu ulaza A T uamplitudu izlaza Z oZo = PZ ⋅ATZa funkcije koje na ovaj načintransformišu (pretvaraju, preslikavaju,prenose) ulaz u izlaz,TZo=i ZZoe γOdnos izlaza i ulaza jei( ωpt+εT)ZeoZo Zoi( ωpt+εT)′T AeATAT TiγZP e P eu tehnici (elektrotehnici, automatskomupravljanju...) odomaćio se terminprenosna funkcija, koji je prihvaćen i ubrodogradnji.U literaturi na engleskom jeziku čestose umesto odgovarajućeg terminatransfer function, za realni deoprenosne funkcije koristi i terminResponse Amplitude Operator, iodgovarajuća oznaka RAOZiγZZ= = = = =Z⋅ζse, umesto odgovarajućeg terminaP Zkompleksna prenosna funkcijaNjen modul je ranije uvedena (realna) prenosnafunkcija P Z , a njena faza je γ ZPREDAVANJA 2009. 97
PONAŠANJE BRODA NA TALASIMA____________________________4.3. Plovidba na bočnim talasimaPretpostavićemo da brod plovi bočno u odnosu naregularne talase...Važiμ = -π/2 , ω p = ω T ,a izraz za slobodnu površinu glasiζ ( η, t) = ζ + A sin( k η+ω t)T VL T T TTalasi se prostiru od pozitivne kanegativnoj osi ηBrod istovremeno vrši valjanje φ(t),poniranje ζ G (t) i zanošenje η G (t)...a nezavisne diferencijalne jednačinekretanja glase( Jx+ m ) ϕϕ + n ϕϕ + gD⋅MG⋅ ϕ = Aϕ sin( ωTt+δϕ)( D+ m ) ζ + n ζ + ρgA ζ = A sin( ω t+δ )ζ G ζ G VL G ζ T ζ( D + m ) η + n η = A cos( ω t+δ )η G η G η T ηAnaliziraćemo, detaljno,samo valjanje broda...PREDAVANJA 2009. 98
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