Dynamics cheat sheet

More documents

Recommendations

Info

$my Latex and Tex4ht cheat sheet$

14 Velocity and acceleration of rigid body 3D 14.1 Using Vehicle dynamics notations F x Nasser M. Abbasi 3d_1.vsd May 26, 2011 L I N F z W z r Linear force torque Linear velocity angular velocity v y p q V x M F y U F Forces, Torques, linear velocities and angular velocities for a general 3D rigid body I xx I xy I xz I yx I yy I yz linear momentum U qW rV F d dt p d dt mvm d dt v m a V rU pW W pV qU U V W p q r F x F y F z L M N d dt H d dt I Angular momentum Derivation of this is much more complicated than with the case of linear motion (F=ma), since m is scalar there, but for rotation, I is matrix. See next page for the derivation 58
14.2 3D Not Using vehicle dynamics notations Nasser M. Abbasi 3d_1.vsd May 26, 2011 z F z Linear force torque Linear velocity v v x v y v z angular velocity v z F x x I v x x x z z y y F y F Forces, Torques, linear velocities and angular velocities for a general 3D rigid body I xx I xy I xz I yx I yy I yz F d p dt d mvm d v m dt dt a y z v x x v z a a x y v z z v y v y y x y z F x F y F z x y z linear momentum a z x v y y v z The derivation of the above is given next, but it uses the standard formula given by d A d A A dt dt resolved This is in the inertial frame of reference This is the same A, but its components are with respect to the body fixed coordinates system, Cross product 59
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 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: 13 Velocity and acceleration of rig
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.
show all

Dynamics cheat sheet

Create successful ePaper yourself

Delete template?

Save as template?