A 5 DOF spacecraft model consists of 3 planar rigid bodies as shown in class. The spacecraft is assumed to be located in

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A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 1 (87.86 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 2 (59.12 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 3 (46.79 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 4 (41.76 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 5 (49.71 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 6 (32.74 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 7 (47.06 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 8 (42.44 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 9 (29.22 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 10 (43.24 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 11 (44.59 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 12 (44.32 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 13 (32.11 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 14 (45.42 KiB) Viewed 17 times

A 5 Dof Spacecraft Model Consists Of 3 Planar Rigid Bodies As Shown In Class The Spacecraft Is Assumed To Be Located In 15 (51.78 KiB) Viewed 17 times

A 5 DOF spacecraft model consists of 3 planar rigid bodies as shown in class. The spacecraft is assumed to be located in deep space away from any gravity fields or other disturbances. The spacecraft model consists of a rigid central body (“Bus") connected via single DOF rotational joints to a pair of rigid solar panels. The elasticity of the solar panels is modelled by placing a lumped torsional spring of spring constant K at the rotational joints between the bus and panels. Damping of the solar arrays will be neglected in the analysis. Thrusters and reaction wheels on the bus are used to generate forces and torques about the center-of-mass of the bus to translate and rotate the spacecraft. 1. Derive the DEOM's of the spacecraft using Lagrange's Equations. Assume the angles associated with the solar panels are small in your derivation 2. Using the system parameter values and initial conditions given in lecture write a MATLAB script to simulate the motion of the spacecraft Use the fixed-step ODE5 integrator provided in class. Provide plots of the time responses of all states in the model for each case simulated 3. Describe and apply some methods to verify the correctness of your results. How do you know that you derived and coded the DEOM's correctly? Describe how the numerical integration step size of the integrator is chosen How do you know the step size has been chosen correctly? 4. Provide a write-up of your derivation of the DEOM's and include your MATLAB code and the plots you generated. You may work with a partner on this project and should only submit one report per team
DYNAMICS OF A 3 BODY SPACECRAFT l l Bus LEFT SOLAR PANEL Rihy SOLAR PANEL N THICROP τ THIN ROD ( CL 08=CB CR ļ Kd د لا n2 Mp = 125 kg a ਹੈ , 4 SAME FOR BOTH PANELS Mo = 2250 kg Ip = 1000 Kg - m2 About CL, CR Io = 2000 Kg.² ABOUT CB l Im d = 6m FUNDAMENTAL fp = 0.1 Hz Free OF TRUEL к NCLUEET Dampal fp = 1 1 1 1 1 p0.25% & Brev
བ། (༦) Og(+) ATTITUDE УА) 9. ہے۔ x(+) M 1 9, = X, 92= Y, Z = 0, at = OL, 1s = OR SYSTEM MODEL HAS 5 DOF's (X,Y) TRANSATIONAL DOS's of Bus (m Og ATTiTvorog Sus (8C, ! ORIONTATION OF To Wan Arrays RELATIUT TO BUS
以 DX LOVERALIZED FORCOS 是 張) 击港 磅) - by - 以 09 二 |Qe 4 是( ) () 0 A| 决、 dt 00 00) ()- : - 0 00g 0px
A. A = 1112 : L = T-u THAT + + - PANEL Т. our = 1/2 Me" Ź Tous ūo. T = Tous TRIGHT PAWEL -MBMB. LCB V + TRANSITIONAL TRICHT {mpovca v R + < Ip Mwa. Mam ROTATIONAL žmp Tante tek wat Roti TOML NOR PANEL = Thiu TIUNIL THAT به ) + ماهه V - PANEL Trauho TIONAL ROTATIONAL
2 Un = xo 2 → ✓ + 12 KOR ? ♡ SYS STRAIN ENELY OF LOFT PANEL STRIN ENERLY OF RIGHT PANEL K tx y mo U = 1 kx² mm STRAN ENERLY OF LINEAR SPRING
ISBL L = 2 Mo (x² + y2) + + IB0? (4 +į mf6z+y+ +1*65* +++ (09 +61)* + 2 týdestij) Sol) + 1 / mp (2010 (66 +61) Col -ady los tor) CBL). +1 mp (*?**? +420g? to listo- 24ě légtör) SoR) + limp 12:46g (igt be cox + 2 dy fyt bie) Com) + 1/2 Ip loo ton )2 + 2 Ip (os + O2)2 - (Eko? + KO) 호 ,? ISBR B 2 where CALAC (89+OL) Soles (ty+ OL) SBR & slegton) Con & C(OBT OR)
PROJECT 1 1. DERIVE L 2. SUBSTITUTE L INTO ALL 5 LAGRANLE'S EQUATIONS GIVEN IN CLASS ON 5/3 PERFORM ALL DERIVATIVE IN ALL 5 EQUATIONS. AFTER STEP 2 LET) DEOM'S) CALCULATIONS
3. MATLAB SIMULATION Otom's PLUGIN NUMBERS HERE CODE МАТИ, (әре Plots / V LENERATE
TOTAL POWER GENERALIZED FORCES ✓ NB V Fous, ant & Mous, ant" + EXT Nu . BUSEXT Psys = + Friday HUR + + RIGHT PR Por, XT PAR, EXT w + FLEFT vo MONT NE? Patur, EXT Mv8 = x PAR, EXT vo 범 xñ + y nz Foun, dar = F in try bez , , Mous, Ext = Thz وحم NB = Of û ng M
こ n A ^ Mows, on tâng. oe nis = tör WEB THB I bo by b3 ceg -Sog ni | SOB Copo ng 10 0 0 1 Fous, ixt = Fx (cop hi ) F7 (se mit eine) = (FX COB - Fysos) + (EXSOB + Fy (98)ůz (kmi ýine) [(fx@p-Fy sepni + (tayan ng - 끼 +
= (fy 10, - Ғуло) х + (F30, + fy @s ) у Ө0) Qy вх и. X5 + + Р. (7 хо, -50, ) х + (fү 50, +hy 10 ) + те, + рік не бу фър 1 , а 1 Oo QORT две QOL о QozF - с |x| (+ | Q, Pz cob - у в (н (ву - 1 750 , +7 (6)
+ À Å. B = (A x ñ + Ayaz ). (Bx M + hym Axbx + Ay by n .^, = 1 ^2. ^2=1 A, ก, - 20
V Eom's FINAL PROJECT (iMaLL SOLAR KRLAY Rothens) M 9 + Ct D a + K9 = Q where 9 LOVERALIZED COORDINATE VECTOR 5x) M MASS MATRIX 5x5 (M=MT) NON-LWEAR ACCELERATION VECTOR 5x1 DAMPINL MATRIX 5x5 2 D-07) (kakt) a sxs STIFFNESS MATRIX k VI 11 LUMALIZE FORCE VE Ztore 5*) WE USUALLY PART THE LAUFALIZED (ory in 771 VECTOR AS LLOWS: х RIGID 31r У. OOPY DOG'S 92 B6 2) If 1 ELлс /FLх 5x1 2 DOF'S. 3 og 94
EÓM'S FINAL PROJECT (SMALL SOUTH ARKAY ANELTS 3 2 2 Z Mer of :: 0 o 0 O 010 PH KH 4 Merliner (Mb + 2 MP M6+ame TI + 2 Ip +2mp (8+)² J rumpaseo mp d sog Mr 're mp a cop -med cog 쓰 3x2 2 Ip + mpd (8+d) I, timp d (ord)] 3x3 0 T Ei क = M fra mit 2x3 2 x 2 Miff = (Ip tmp d² I 2x2 ) KIO 2x2 DER - [1], KTE KH = [tex] 2x2 impo{(og +01) - 0g + ón)?} COB modz (68 +0,1² - log + Onl?} soo 0 TOR Qx QY 9ra [] 96= [r BOB 2 2x 3x! 3x !