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Spacecraft and Aircraft Dynamics

Spacecraft and Aircraft DynamicsMatthew M. PeetIllinois Institute of TechnologyLecture 9: 6 DOF Equations of MotionAircraft DynamicsLecture 9In this Lecture we will cover:Newton s Laws ~Mi=ddt~H ~Fi=mddt~vRotating Frames of Reference Equations of Motion in body -Fixed Frame Often ConfusingM. PeetLecture 9:2 / 24 Review: Coordinate RotationsPositive DirectionsIf in doubt, use the right-hand :Positive DirectionsFigure:Positive RotationsM. PeetLecture 9:3 / 24 Review: Coordinate RotationsRoll-Pitch-YawThere are 3 basic rotations an Aircraft can make: Roll = Rotation aboutx-axis Pitch = Rotation abouty-axis Yaw = Rotation aboutz-axis Each rotation is a one-dimensional two coordinate systems can be related by a sequence of 3 PeetLecture 9:4 / 24 Review: Forces and MomentsForcesThese forces and moments have standard labels.

Using Calculus, this concept can be extended to rigid bodies by integration over all particles. M~ = X i M~ i = d dt H~ Definition 3. Where H~ = R (~rc ×~vc)dmis the angular momentum. Angular momentum of a rigid body can be found as H~ =Iω I where ωI =[p,q,r]T is the angular rotation vector of the body about the center of mass. • pis ...

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