Dynamics cheat sheet

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$my Latex and Tex4ht cheat sheet$

Algorithm 1 Hohmann Walking Rendezvous Orbit, case 1 1: function hohmann walking rendezvous(θ 0 , r, altitude, µ) 2: θ 0 := θ 0 π 180 ⊲ convert from degrees to radian 3: r a := r + altitude 4: T := 2π√ r 3 aµ ⊲ period of circular orbit 5: n := 1 6: done:=false 7: while not(done) do ( 8: TOF := N − θ 0 9: a := solve 10: r p := 2a − r a 11: if rp < r then 12: N = N + 1 13: else 14: done:=true 15: end if 16: end while 2π ) T ( T OF = 2π √ 17: V befor := µ h √ 18: V after := µ ( 2 h − 1 ) a 19: ∆V := 2(V after − V before ) 20: return (TOF, ∆V ) 21: end function √ An example implementation is below ) a 3 µ for a 1 hohmannRendezvousSameOrbit[\[Theta]00_, r_, alt_, mu_] := 2 Module[{\[Theta]0 = \[Theta]00*Pi/180, n = 1, delT, v1, v2, period, a, 3 rp, ra, done = False, vBefore, vAfter}, 4 ra = r + alt; 5 period = 2 Pi Sqrt[ra^3/mu]; 6 While[Not[done], 7 delT = (n - \[Theta]0 /(2 Pi)) period ; 8 a = First@Select[a /. NSolve[delT == 2 Pi Sqrt[a^3/mu], a], Element[#, Reals] &]; 9 rp = 2 a - ra; 10 If[rp < r,(*we hit the earth, try again*) 11 n = n + 1, 12 done = True 13 ] 14 ]; 15 vBefore = Sqrt[mu/h]; 16 vAfter = Sqrt[mu (2/h - 1/a)]; 17 {delT, 2 (vAfter - vBefore)} 18 ] And calling the above 82
1 mu = 324859; 2 alt = 1475.776; 3 r = 6052; 4 \[Theta]0 = 3.80562; (*degree*) 5 hohmannRendezvousSameOrbit[\[Theta]0, r, alt, mu] 6 {7123.89, -0.0467913} 18.11.2 Two satellite, separate orbits, rendezvous using Hohmann transfer, coplaner 83
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Dynamics cheat sheet Nasser M. Abba
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18.7.2 Bi-Elliptic transfer orbit .
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are the natural frequencies of the
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Similarly, µ 2 is found ⎧ ⎫T
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Or in full form and ⎧ ⎫ ⎡ ⎨
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Hence The first eigen vector is Sim
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The transformation from modal coord
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Where F n = 2 T F 0 = 2 T ∫ T 0
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Let z = Re { Ze iωt} , z ′ = Re
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Now, u = Re { Ue iωt} , u ′ = Re
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Hence at t = 0 the phase of the res
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The following table gives the solut
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5.3 no loading (free) mu ′′ + c
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5.5 Impulse sin function Input is g
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Solution to single degree of freedo
Page 31 and 32: 7 Some common formulas These defini
Page 33 and 34: 8 Derivation of the solutions of th
Page 35 and 36: 8.2.2 under-damped ζ < 1 The gener
Page 37 and 38: When ϖ ≈ ω but less than ω, le
Page 39 and 40: Hence the full solution is u p = p
Page 41 and 42: 8.4 Response to impulsive loading 8
Page 43 and 44: where A = B = F 0 m 2ω √ ξ 2
Page 45 and 46: where ∆ is very small positive qu
Page 47 and 48: at t = t 1 ˙u (t 1 ) = −ξωe
Page 49 and 50: 8.5 references 1. Vibration analysi
Page 51 and 52: 11 Formulas sin 2 x 1cos2x 2 cos 2
Page 53 and 54: 12 Velocity and acceleration diagra
Page 55 and 56: 12.3 spring pendulum with block mov
Page 57 and 58: 13 Velocity and acceleration of rig
Page 59 and 60: 14.2 3D Not Using vehicle dynamics
Page 61 and 62: 14.2.2 Derivation for τ = Iω in 3
Page 63 and 64: 15 Wheel spinning precession x Mg
Page 65 and 66: 18 Astrodynamics 18.1 Ellipse main
Page 67 and 68: magnitude of ⃗r period T mean sat
Page 69 and 70: 18.3 Flight path angle for ellipse
Page 71 and 72: This diagram below from Orbital mec
Page 73 and 74: 73
Page 75 and 76: 18.7.3 semi-tangential elliptical t
Page 77 and 78: 18.8.1 Rocket equation with plane c
Page 79 and 80: 18.10 interplanetary transfer orbit
Page 81: 2. Find speed of second planet V 2
Page 85 and 86: 18.11.3 Two satellite, separate orb
Page 87 and 88: 1 TOF:=hohmann_rendezvous_2(theta=0
Page 89 and 90: 89
Page 91 and 92: 18.14 Orbit changing by low contiuo
Page 93 and 94: C r below is the core chord of the
Page 95 and 96: 1 C L = ∂C L ∂α α = C Lα α
Page 97 and 98: 1 2 3 C Lwb = ∂C L wb ∂α wb α
Page 99 and 100: 2. stall from http://en.wikipedia.o
Page 101 and 102: http://en.wikipedia.org/wiki/Flight
Page 103 and 104: http://www.grc.nasa.gov/WWW/k-12/UE
Page 105 and 106: http://en.wikipedia.org/wiki/Lift_c
Page 107 and 108: http://adamone.rchomepage.com/cg_ca
Page 109 and 110: From http://www.solar-city.net/2010
Page 111 and 112: Page 184, flight dynamics principle
Page 113 and 114: Image from http://www.americanflyer
Page 115 and 116: From FAA pilot’s handbook I do no
Page 117 and 118: zero-lift angle The angle of attack
Page 119: Image from http://www.aerospaceweb.
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