Dynamics cheat sheet

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$my Latex and Tex4ht cheat sheet$

tail mean aerodynamic chord The whole Airplane neutral point (aft c.g. for static stability) Wing mean aerodynamic chord km forces.vsd updated 2/3/ 14 Nasser M. Abbasi 19.2 Summary of main equations This table contain some definitions and equations that can be useful. # equation meaning/use 94
1 C L = ∂C L ∂α α = C Lα α = aα C L is lift coefficient. α is angle of attack. a is slope ∂C L ∂α which is the same as C Lα 2 C Lw = C Lwα α wing lift coefficient 3 C D = C Dmin + kC 2 L drag coefficient 4 C mw = C macw + (C Lw + C Dmin α w ) (h − h nw ) + (C L α w − C Dw ) z¯c pitching moment coefficient due to wing only about the C.G. of the airplane assuming small α w . This is simplified more by assuming C Dw α w ≪ C Lw and (C L α w − C Dw ) ≪ 1 5 C mw = C macw + C Lw (h − h nw ) simplified wing Pitching moment C mwb = C macwb + C Lwb (h − h nw ) 6 = C macwb + ∂C L wb ∂α wb α wb (h − h nw ) = C macwb + a wb α wb (h − h nw ) simplified pitching moment coefficient due to wing and body about the C.G. of the airplane. α wb is the angle of attack 7 C Lt = Lt 1 2 ρV 2 S t C Lt is the lift coefficient generated by tail. S t is the tail area. V is airplane air speed 8 L = L wb + L t total lift of airplane. L wb is lift due to body and wing and L t is lift due to tail 9 C L = C Lwb + St S C L t coefficient of total lift of airplane. C Lwb is coefficient of lift due to wing and body. C Lt is lift coefficient due to tail. S is the total wing area. S t is tail area 10 1 M t = −l t L t = −l t C Lt 2 ρV 2 S t pitching moment due to tail about C.G. of airplane 11 C mt = Mt = − lt¯c S t 1 2 ρV 2 S t¯c S C L t = −V H C Lt pitching moment coefficient due to tail. V H = lt¯c S t S is called tail volume 12 V H = lt¯c S t S ¯V H = ¯l t¯c S t S introducing ¯V H bar tail volume which is V H but uses ¯l t instead of l t . Important note. V H depends on location of C.G., but ¯V H does not. ¯lt = l t + (h − h nwb ) ¯c 95
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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
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7 Some common formulas These defini
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8 Derivation of the solutions of th
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8.2.2 under-damped ζ < 1 The gener
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When ϖ ≈ ω but less than ω, le
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Hence the full solution is u p = p
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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 and 82: 2. Find speed of second planet V 2
Page 83 and 84: 1 mu = 324859; 2 alt = 1475.776; 3
Page 85 and 86: 18.11.3 Two satellite, separate orb
Page 87 and 88: 1 TOF:=hohmann_rendezvous_2(theta=0
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Page 91 and 92: 18.14 Orbit changing by low contiuo
Page 93: C r below is the core chord of the
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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Dynamics cheat sheet

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