Dynamics cheat sheet

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$my Latex and Tex4ht cheat sheet$

F ma linear momentum p mv F d p dt particle kinetic energy T 1 2 mv2 I angular momentum H I cg d dt H rigid body T 1 Mv 2 cg 2 1 I 2 2 cg my 2 n y n 2 y fy,t y cy k m y fy,t n For small epsilon 1 1 1 1 1 1 k m ,c 2 n m conservation of angular momentum d dt H constant x n2 x 0 If n 0 then sinusodial solution, ok if n 0 then solution blows up, exponential 52
12 Velocity and acceleration diagrams 12.1 Spring pendulum Length of pendulum fixed Length of pendulum changes with time 2L L L L Velocity diagram acceleration diagram L 2 L Lt L 2 L L Velocity diagram acceleration diagram y Length of pendulum changes with time and base of pendulum moves ÿ x x y L x L 2 ÿ L x 2L Velocity diagram L acceleration diagram r Nasser M. Abbasi Oct 10, 2013 (drawing2.vsd) 53
Page 1 and 2: Dynamics cheat sheet Nasser M. Abba
Page 3 and 4: 18.7.2 Bi-Elliptic transfer orbit .
Page 5 and 6: are the natural frequencies of the
Page 7 and 8: Similarly, µ 2 is found ⎧ ⎫T
Page 9 and 10: Or in full form and ⎧ ⎫ ⎡ ⎨
Page 11 and 12: Hence The first eigen vector is Sim
Page 13 and 14: The transformation from modal coord
Page 15 and 16: Where F n = 2 T F 0 = 2 T ∫ T 0
Page 17 and 18: Let z = Re { Ze iωt} , z ′ = Re
Page 19 and 20: Now, u = Re { Ue iωt} , u ′ = Re
Page 21 and 22: Hence at t = 0 the phase of the res
Page 23 and 24: The following table gives the solut
Page 25 and 26: 5.3 no loading (free) mu ′′ + c
Page 27 and 28: 5.5 Impulse sin function Input is g
Page 29 and 30: 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: 11 Formulas sin 2 x 1cos2x 2 cos 2
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
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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