test_1_FA05_KEY

test_1_FA05_KEY - -a.a{i —[l.3 l(25 points Given the DCM...

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Unformatted text preview: -a.a {i —[l.3 l. (25 points] Given the DCM g” = [l l i) {LS [II “0.6 A a. {2 pts} What is the axis ofrotation ﬁoni I to S '? {51,52,0i‘ilj b. [5 [its]: Calculate the angle between anti 5?, IS. A ,._. E. :C 1, 45‘:L4|11+C|L?1+C|515 —" A asst ’l. +E,-’CZ)”E.L+ (35,. Li}: L(§h15)‘= {Tots-it: : W3 .3 l3 c. [8 pts) If the acceleration of an object wrt frame I is E = 1611+ mi2 + of}, then calculate this acceleration in terms of the .El. vectors. r9 If: ﬁll-Pi m Else: C an: _..—.. Fril— rl _._.. _— _ r—O.L£+U%c r W1 L {REF fol. a ﬂew cf : ('eiﬂnﬂzihlﬁ, + m§l+(o.31-O.£n)§3 .m .... Inc d. {111} pts] Which of the following CANNOT be a DEM? Circle all that apply. {lJDTl — ﬂﬁﬂﬂ CI = [IIJDTl {IT’CITI U [i II] 1 |"o . [25 points) A satellite is rotating about its ii: axis at constant rate {on wrt the inertial frame bl, as ShDWI] in the ﬁgure. A tube {with negligible mass) mounted on the satellite can be rotated about the b3 axis by the amount 6' and at rate I? . The coordinate system T is deﬁned such that fl is aligned with the tube‘s axis, and E3 is aligned with 333. — t N a} [3 pts) Develop the expression for the angular velocity of T wrt N, n:- [expressed interms ofjusttbe F; vectors.) C cﬁl 5.9 c, .rT' :‘BM _-‘T‘E __ = -59 3 {A} thl: L23 'l' [A o to o J'- .. ' 1: all): + 8%; TL ("CE __Sg3. 0] JN " *’“ s = L " (A) :tswsE/‘ﬁ + mace!le [9113 b.) (3 pts) At some instant in time t“, d3” = it'll + ml: + ﬂ."l . Find (Elm in terms ol‘tlie br- 1rectors at that time. A f“ I. no .: an t ant—33 SE" 0‘ = W‘s” {continued on next page) 3. [25 points) lCtrbital properties a) (14 pta) lCircle all of the quantities that are constant for a satellite in the two- body problem [i,e., gravity from a central source is the only force acting on the satellite) a (orbital ener E [velocity vecto r} {3’ (true anomaly} ,.-«;F‘"""'—“‘——_""_"H."'__. E h (orbital angular momentumm {p (semidlatus rectum} > F {radius vector] b} [I 1 pts} A satellite is injected into an Earth-orbit at m = 39% km, with speed v9 = 3.1 knifs. Calculate the value of flight~path angle a” such that the orbit will have a periapsis radius rp = T343!) km. The angle 95 is measured from the plane perpendicular to F , in the clockwise direction, to the velocity vector 11 . Note that at periapsis, 96p = U. Also, angular momentum can be calculated as h=rvcos¢t 1|: L 5: if was. s (3" Tm) , “BET??- were? 2: r" EL WGDl-cm E” = was rte/51 10% warm, 8 e viii! warms?” J Ezrii.qELM1};L=£F/&L_ H _ f *1 1 r i L: 1 f, -— Q73fq rim/Ig- '! '- - I la. ." “BI-31‘ I ,III.J. p g} 44"; r 'sﬁr' tiliirjf K r”;: '/ n- I? I 2 I37é7fﬁ=5m 5': ha: FDUDCoE a (—3» x '3'..- Illgfp‘ l {’5’ 5:12;: one”? ——~r*"t c.) (9 pts} A mass or moves inside the tube, with position given by F = r31 , whore r is a funotion of time. Calculate the inertial velooity ofm For any.r possible timo. T r- . " F t i.— if: AF : rcél l)B‘I'JI.J'}{..IF : t 2. _5 IE Loﬁsﬂ mﬂco [9 H __ _ J: :Ti: .i ﬁ-Tﬂg? 1” 0 t:- cUZ Adi - b A : ("ﬂ—[Ea "' FRI” ca'ﬁs 4. (25 paints.) Givcn initial conditions far a satcliitc in Earth-orbit, in terms cf :1 set 01" the unit vectors r'iurizz F = 5223a: +5344ﬁ2ﬂmt] v = —5.4ﬁ 1p”:I + 6.1ﬂgﬁlikmfs} r iii-“1:4 FLT“ 2, Lin-'1 "h" “cf-Ar U? 3r”? Elm/1r. Calculatc: a) [5 pts} the orbital cncrgy g : _.’,£‘L_ r“ g : ‘2i. km'I/ft 1.- 2 b) {5 pts} Eccentricity 1u'cctnr in tcrrns cf the El , ii: VECIGTS. ,__, ___ __ {x A A IAK = r»: U I '-\r'|U?_.—raui)ﬁ3 =53¥§ZJ§ 15m13~_ﬂ3 hi; : Wham:th : 3::34922 ﬁ, +32hcfé7bzéﬁ‘liﬂ .—"II- ” A 51 E- : mix _ I; * 0.5?H7m+DEW“;31—0.7i?33|—D.£i¥7ﬁ2 ﬂ r~ ‘11gto.rqz#n1+o.mmz {continued cn next pagc} e] (5 pts) orbit type [eirele®arabela, hyperbole} d) {ltlI pts] ease? for the position vector F given abeve. = (mate?! it +0.1ng 32) . (15223 3;; + 301% Earl” (012'36 Nazareth) . = , W73 I meme; shin; Us}: or-LH— is?” l ifeﬂa O '.l r:._._3,3——-—-—‘I+EIC‘EB 'P:[;LU_E1-) :1 = 33% — ﬁtment 6: = "Heinz = 9,212; e} (BONUS: 5 pts} There are 2 possible 1values ef 49 that weuld satis 1-; year 4: anewer to part d}. What other infennatien can be used te determine which 1value 1;) : EFL?- [ ef 9 is eerreet?r PM 0 <5: -: twig... r— is‘ Eesrtive r: 2 Hi? ...
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test_1_FA05_KEY - -a.a{i —[l.3 l(25 points Given the DCM...

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