Equations of Motion with Wind
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Video Lecture 5 of 8
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### Lecture Description

In this lecture Dr. Ir. M. Voskuijl first continues his lecture on cruise flight. He starts with the analytic solution for the range of cruise flight, followed about a story about the global flyer which flew around the world. Next the weight breakdown of aircraft is discussed and its effect on range. Of course range is only part of the story, as it is greatly intertwined with the price of fuel and the money earned for a flight, so the economics are discussed. Then the main topic of the lecture is addressed, deriving the general equations of motion of aircraft including wind. To do so a new set of axis systems is explained, the earth,the body and the air path axis system. To be able to transform between these axis systems, vector notation is used. Accelerations and forces are then explained in these new axis systems, and with these known, the complete set of equations of motion can be written down.

### Course Description

Course Contents:
1. Turning performance (three dimensional equations of motion, coordinate systems, Euler angles, transformation matrices)
2. Airfield performance (take-off and landing)
3. Unsteady climb and descent (including minimum time to climb problem)
4. Cruise flight and transport performance
5. Equations of motion with a wind gradient present
6. Equations of motion applied to various phases of space flight
7. Launch, Vertical flight, delta-V budget, burn out height, staging
8. Gravity perturbations to satellite orbits, J2 effect for low earth orbit satellites, J2,2 effect for Geostationary Earth Orbit satellites leading to contribution in V budget
9. Patched conics approach for interplanetary flight, gravity assist effect / options for change of excess velocity (2d, 3d), Launch, in orbit insertion.

Study Goals:
1. Integrate fundamental disciplines (aero, power and propulsion, mechanics..) to describe the kinematics of aerospace vehicles satisfying real world constraints
2. Derive equations of motion for elementary flight and mission phases (climb, turn, cruise, take-off, launch, orbit)
3. Derive analytical expressions for optimal performance (steepest turn, Breguet Range, patched conics, J2, maneuvers )
4. Determine pros/cons of multi-stage launchers.
5. Assess sun lighting conditions on a satellite.
6. Determine the influence of wind (gradient) on aircraft motion and performance.
7. Develop the theory to describe an interplanetary trajectory as a succession of two-body problems, and apply this concept to real missions.