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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. The Forces are:XAxial ForceNet Force in the positivex-directionYSide ForceNet Force in the positivey-directionZNormal Force Net Force in the positivez-directionM.

Equations of Motion • How to differentiate Vectors in Rotating Frames • Derivation of the Nonlinear 6DOF Equations of Motion Euler Angles • Definition of Euler Angles • Using Rotation Matrices to transform vectors • Derivatives of the Euler angles I Relationshiptop-q-rinBody-FixedFrame M. Peet Lecture9: 23/24

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