Modelling of A Helicopter System

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1 Modn of A Ho m nn u of nnn n Unv o London London W 6B, U -m: Ab ond modn nd muon ud of o m UH-6 B H o Mm mod of n mn oo o nd n o onvnn of non, fo nd momn on of vou o omonn vn n o bd n mod o mod of UH-6 B H o o muon ud UH-6 b GM mod (Gn oof Mod) ud omon md bn muon u nd f d A n mn bu dmn nd nom ou, u d o v non Ov mod n UH-6 B H o mod n b ud fo ono dvomn o mov f ndn u nd fomn od - modn; muon; mod vdon; o m; f ono NODUON A o d of fdom n moon: u/don, fo/f (onudn moon), f/ ( moon), n, on, nd n moon of o vd b; ) ov nn of mn oo d, u nn oo u (ov ); ) nn nuod funon of mu --n fo/f o f/ nd n u vo don ( ); nd ) ov nn oo, n oo u nd u momn A o o mu munou ono fo nd momn, n, ono of o, dffu ndd A o o do o ono bo fo/f moon ( ono) nd f/ moon (o ono), ov v o ono u nd don moon (v ono), nd d o ono f nd n moon ( ono) Lf, u, n, nd on ono om fom mn oo n ono om fom oo (Bm, 976, n,, 98) An dnm om of onon o nd o dvo ono m fo vn om n o dv dnm mod fo o dnm mod oud b ud o nd ono n, m nvov nd uon of moon bou o ubum oon n foon on mm mod of n mn oo o nd fo nd momn fom dffn mn of o dud n d n mod of UH-6 o bn dvd nd muon ud bn ondud u nd n DNAM MODL O A HLO ov v uon of moon dvd fo nd momn fom dffn mn of o, u mn oo, oo, fu nd mnn, dud n o d of fdom n moon nd nn v n n, u, v, f vo omonn n of v,,, f o, nd bou bod fn, nd,, u n o dv uon of non nd oon moon of o, o umd o b d bod fd o n m fd n of m of f, o mov m vn vo omonn und on of d fo u n dfn onon of fu o m (dfd, 996) fou ono nu,, onudn ( ), ( ), ov v ( ) nd d nu ( ) ono o moon ou X,,, L, M, nd N o m uon foo u v n X / M () v u o n / M (b) u v o o / () M N L L M () (b) N L ()

2 n o n n () n o (b) o n () M nd m of o nd on du o v,,, momn of n of o bou, nd, nd f odu of n mod () ~ () n b ondd d onnon nonn m,, foon fom: f, () U G, f (5) ov n fo X, nd on,, nd momn N M L,, bou,, n b n X X n o (6) A N N N N v (7) X o n (8) nd N N N N N b L (9) M b M o n n o () N N N N N N b N () dn, nd mn oo d du nd d, nd mn oo d f uv o nd od, nd,, mn oo fo offn n f vn b W XW X o n n o () ) ( () W d- n nd mn oo u offn vn b () mn oo fo offn n ub-nd XW nd W n b obnd ou uon (5) nd (6) n m of mon omonn of nd d odnm od nd mon of fn () () () () () XW (5) () () () () () W (6) onn n nd, f mon fn n mon omonn of nd d odnm od vn b foon on () (7) () (8) () (9) () () () () () 8 ()

3 () 8 () mn oo ov nd vn b n () n uon (), nd ov n onn, nd n uo fd b n nd f nom on nmn, nd ov v v (ono nu), d omonn n ub-nd dfnd b o n n o, (5), onudn nd dmnd b n o (6) n o, (7) nd,, fdb n, nd fd fod n, nd onn, dju b o nd, nd onudn v (ono nu) oo ovd ono fo, o on on o ovd d u fo nd b odu n momn bou mn oo f (Nmn, 99, Lmn, ) onbu n fo, momn L, nd M ( uon (7), (9) nd ()) oo onbuon n b dmnd b n n, (8) oo (ono nu) nd vn b H (9) n uon (9),, d n onn, nd d n onn, ov v v nd d v, ono nu Amo of fomn of o dnd on o-n fomn (ou, 986) H mfd mod fo o oo-d, od nn nd oo ovno dnm fomu nd foo G () () () () n m domn, dffn uon n b n (), nd nn, mn oo, nd oo ou, v G oo o momn of n of on m dn oo d nd ov nn/oo d n om umon md o odu od fom of on o o moon, on bo oo fn nod o mn oo, fn n umd m nd ov fu on nd d ff nd nd d, umd m omd oo nu n nm of d moon, b umon dn o oo d odnm ummd foo: A onn, o-dmnon, f uv o umd om ff nod nd vd fo ff nod ndud vo dbuon, nom o oo d, nud n onudn nd von, vu n fn m momnum ondon oun fom d nd dnm no fn moon nod u-d fn nd onn ud n dvon of on fo nd momn on fu,, non of d mod fu mod nd umon m o o n odnm odn n nd n odu od fom of on fo oo fo nd momn

4 MULAON UD O UH-6 BLA HAW HLO UNG LGHLAB A m o bn n fo modn mn oo nd oo fom oo fn bn nod n b, oo omonn mmnd bd on mfd o mod of dmnn of fn oo n fod f (o No 76 Non Advo omm fo Aonu b J B, J,) d oo o-odn m of oo X fod no f-m fo nd n don of u oo u nd ou ud funon of d o fo b mn m umon mnond bov B dvd oo u nd ou b n nn -od ov oo d n nd vn m ov mu o oo, un on n vu fo oo u, u offn momnum o n b ud fom (5) on dffn fom mm mod dbd n (8) o ff,, nodud du o fn ondon o nfo nd ndud vo v n b ud b (6) v (7) Un vu, n v odu fomd o dmn vu of o nfo don b un uon bo dvd b n momnum o v,,,, (8) nd d ov oo nd, v o nfo o oo d vu,, nd, omud b, B (9), B B (), B B (), On vu of,, nd, v bn dmnd n, on on, ndud vo n ud un bov uon om uon (6) u offn n ud un v () oo u n n b ud foon uon: 8, () o ff,, du o fn ud o modf oo u funon of vo vn b, u A b b, u A v () v b, A v u (5) n uon () nd (5) non vo, v nd o onn, b nd b, fd b u o un oo ov b n 8, (6) b ommndd oo ov, b ov b, oo u, nd n n fo -f oun n ddon, fo mn oo, n b mod, odnm ff bn n no oun n mo d, odnm omonn num omonn o omuon of od, nfo, nd nfn Aod omud o v moon of d uu omonn nd nfo omud bd on od Addon, nfn bn odnm omonn n b omud u nd mnn omonn mmnd n b mod, b un m odnm, n fo nd momn fom mn vn b funon of ndn nd d n n o of modn du o om fo fd ound o fu nd non of mn oo fu, om dffu ud o onu fo nd momn uon o d u fom nd unn d d fom vou ou ud (B, 96, Won,, 975) nn ouu ou onod b ovno m n n n oo d nd dmnd fu fo n fu n f nd n, (7) f f nd m onn nd n v o of doo n oo d fom f d o mmum onnn fu fo nd, (8) n n oo d nd f d oo d, v nn ou on o

5 fu fo n dbd b ondn o fu fo nd fo, (9) f f n nd, m onn ombnn bov u v ond od odn dffn uon foo (5) uon fu nomd b mmum nn ou m (5) W (5) W m m m (5) m oo d mmum onnn fu fo m n mm mod mfd f ubn nn uon o nd ( uon ()) n f ono m, n, n fom, ov v nd d nmd o mn nd oo d n-n bn ov v, mn oo, nd oo ov o nood n mm mod o nd n ombnd o n fom on nd uom f ono m nd d ou f od uo nm n fom nd ud o o odu fdb ono of o ou, ou onudn nd ou oo ov d fod n o nood n oo fo omnon o nom on fd b no mn oo ov nn o du dv oo n momn fod d n b mod ono omonn dnd mu nu/ mu ouu, n nd nonn ub m muon u nd n o m fo UH-6 o ud n muon ud nd n nd A~A omon u o n mn bn f d nd b GM mod muon u f d nd fom ondud fo UH-6 o und v m nd ondon Nv o ndn, fon n mb 99 (, 99,, 995) muon o dnm mnouv (Hov nd 8) fo fou ono nu bn d ou mod on omud un u f mud ono oon Bo f d nd muon d od n m, n n m omon of v of n, u non vo ( u, v, ), oon vo (,, ), u n (,, ) nd bod on (,, ) n onudn nu muon u oon n m, on n () nd (b) o onudn nu ud o dv mod n ov ondon nd 8 fod f d on ood oon f d on, ov om dn vdn n () n ood mn bu nd o dff n on m, m b n ndon of om un fo n f v v no bn nudd no mm mod ONLUDNG MA db modn nd muon ud of o m mm mod fo o bn dvod fo muon ud nd ono n o muon ud n UH-6 b GM mod bn ud mod on omd UH-6 f d n bo ov nd 8 fod f ondon oon n mn fo bu nom n o on fo o nom ud Ov fo u vd muon n mm mod f un undon nd u b nvd fo n of m nd ono N [] B, J, Moud, JL, nd,, Wnd unn on o fu o fu, NAA N-D-5-8, 96 [] Bm, A, Ho Dnm, dd Anod 976 [], JW, dnfon of UH-6 dvv mod n ov fom f d, AH, M 99 [], JW, A mod uu fo dnfon of n mod of UH-6 o n ov nd fod f, NAA M 6, Auu 995 [5] Hb, B, A Mm Mod of UH-6 Ho, NAA M-8589, 98 [6] Lmn, G, n of Ho Aodnm, mbd Unv [7] Nmn,, oundon of Ho, Anod, A mmb of Hodd Hdn Gou, London 99 [8] dfd, GD, Ho Dnm nd ono, B n Ld, 996 [9] ou,, Ho fomn, nd ono, W u, 986 [] W n nd N, o-wn Aodnm, Dov uon, n, N o, o, 98 [] J Won nd Mn, Wnd unn nvon of o oo ff on o fu mod, NAA M-X- 85, 975

6 u () omon of o dnm on ov bn f d nd G mod fo onudn nu u (b) omon of o dnm on 8 bn f d nd G mod fo onudn nu

7 ANDX A AAM O UH-6 HLO UH-6 o d d fom vou ou nd bo ( Hb, 98) A Af m nd n: A mnn: Don mbo UH-6 Un vu m of o M 55 b Don mbo UH-6 Un vu n 5 f f o n 569 u f f uv o o ndn - f n f n u f 7 u f Loon f of fu fn on fn, 7 f N N f f odu of n 67 u f n of v oon - (6 7) f u fn - (6 ) f A oo ou: A Mn oo ou: Don mbo UH-6 vu Un mn oo d 7 d / mn oo d du 68 f d f uv o 57 d mn oo od 8 - oo f fod 56 d oo u offn 86 - numb of d b - d o numb oo n numb f fun o - - n d - d o-odn of oo 5 f ub mn n 75 d d od 7 f fn n on oon fdof fu f on ffn numb - f - d of d -6 - offn dn 7 u / f Don mbo UH-6 Un vu oo d du 55 f oo d 6 d / d f uv o oo od fn o fo oo n numb f fun o oo oon f of fu fn on Nv o-odn of ub n d 57 d ( n ) ( ) - 7 f 5 f -8 d Numb of oo d b - d of d offn -6 - d f dndn d offn - /f oun ( ) 7 - d o numb 78 - d fn momn of n u f

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