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Dynamics cheat sheet

October 14, 2017   Compiled on December 2, 2018 at 3:21pm

1  Vibration
 1.1  Modal analysis for two degrees of freedom system
  1.1.1  Step one. Finding the equations of motion in normal coordinates space
  1.1.2  Step 2. Solving the eigenvalue problem, finding the natural frequencies
  1.1.3  Step 3. Finding the non-normalized eigenvectors
  1.1.4  Step 4. Mass normalization of the shape vectors (or the eigenvectors)
  1.1.5  Step 5, obtain the modal transformation matrix \(\Phi \)
  1.1.6  Step 6. Applying modal transformation to decouple the original equations of motion
  1.1.7  Step 7. Converting modal solution to normal coordinates solution
  1.1.8  Numerical solution using modal analysis
 1.2  Fourier series representation of a periodic function
 1.3  Generating Transfer functions for different vibration systems
  1.3.1  Force transmissibility
  1.3.2  vibration isolation
  1.3.3  Accelerometer
  1.3.4  Seismometer
  1.3.5  Summary of vibration transfer functions
 1.4  Solution of Vibration equation of motion for different loading
  1.4.1  common definitions
  1.4.2  Harmonic loading \(mu^{\prime \prime }+cu^{\prime }+ku=F\sin \varpi t\)
  1.4.3  constant loading \(mu^{\prime \prime }+cu^{\prime }+ku=F\)
  1.4.4  No loading (free vibration) \(mu^{\prime \prime }+cu^{\prime }+ku=0\)
  1.4.5  impulse \(F_{0}\delta \left ( t\right ) \) loading
  1.4.6  Tree view look at the different cases
  1.4.7  Cycles for the peak to decay by half its original value
  1.4.8  references
2  Dynamics equations, kinematics, velocity and acceleration diagrams
 2.1  Derivation of rotation formula
 2.2  Miscellaneous hints
 2.3  Formulas
 2.4  Velocity and acceleration diagrams
  2.4.1  Spring pendulum
  2.4.2  pendulum with blob moving in slot
  2.4.3  spring pendulum with block moving in slot
  2.4.4  double pendulum
 2.5  Velocity and acceleration of rigid body 2D
 2.6  Velocity and acceleration of rigid body 3D
  2.6.1  Using Vehicle dynamics notations
  2.6.2  3D Not Using vehicle dynamics notations
  2.6.3  Acceleration terms due to rotation and acceleration
 2.7  Wheel spinning precession
 2.8  References
 2.9  Misc. items
3  Astrodynamics
 3.1  Ellipse main parameters
 3.2  Table of common equations
 3.3  Flight path angle for ellipse \(\gamma \)
 3.4  Parabolic trajectory
 3.5  Hyperbolic trajectory
 3.6  showing that energy is constant
 3.7  Earth satellite Transfer orbits
  3.7.1  Bi-Elliptic transfer orbit
  3.7.2  semi-tangential elliptical transfer
 3.8  Rocket engines, Hohmann transfer, plane change at equator
 3.9  Spherical coordinates
 3.10  interplanetary transfer orbits
  3.10.1  rendezvous orbits
  3.10.2  Semi-tangential transfers, elliptical, parabolic and hyperbolic
  3.10.3  Lagrange points
  3.10.4  Orbit changing by low contiuous thrust
  3.10.5  References
4  Dynamic of flights
 4.1  Wing geometry
 4.2  Summary of main equations
  4.2.1  definitions
 4.3  images and plots collected
 4.4  Some strange shaped airplanes
 4.5  links
 4.6  references