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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.

Approach: From Lecture 4, any two coordinate systems can be related through a sequence of three rotations. Recall these transformations are: Roll Rotation (φ) : R1(φ) = 1 0 0 0 cosφ −sinφ 0 sinφ cosφ Pitch Rotation (θ): R2(θ) = cosθ 0 sinθ 0 1 0 −sinθ 0 cosθ Yaw Rotation (ψ): R3(ψ) = cosψ −sinψ 0 sinψ cosψ 0 0 0 1

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