General report

Dynamics cheat sheet

December 2019 Compiled on May 2, 2022 at 12:30am

1 Vibration

1.1 Modal analysis for two degrees of freedom system

1.2 Fourier series representation of a periodic function

1.3 Generating Transfer functions for diﬀerent vibration systems

1.4 Solution of Vibration equation of motion for diﬀerent loading

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

2.5 Velocity and acceleration of rigid body 2D

2.6 Velocity and acceleration of rigid body 3D

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

3.8 Rocket engines, Hohmann transfer, plane change at equator

3.9 Spherical coordinates

3.10 interplanetary transfer orbits

4 Dynamic of ﬂights

4.1 Wing geometry

4.2 Summary of main equations

4.3 images and plots collected

4.4 Some strange shaped airplanes

4.5 links

4.6 references

1.1 Modal analysis for two degrees of freedom system

1.2 Fourier series representation of a periodic function

1.3 Generating Transfer functions for diﬀerent vibration systems

1.4 Solution of Vibration equation of motion for diﬀerent loading

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

2.5 Velocity and acceleration of rigid body 2D

2.6 Velocity and acceleration of rigid body 3D

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

3.8 Rocket engines, Hohmann transfer, plane change at equator

3.9 Spherical coordinates

3.10 interplanetary transfer orbits

4 Dynamic of ﬂights

4.1 Wing geometry

4.2 Summary of main equations

4.3 images and plots collected

4.4 Some strange shaped airplanes

4.5 links

4.6 references