Space Vehicle Dynamics 🛰 Lecture 12: Rigid body kinematics. Rotation matrices. Direction cosine matrix. To describe the orientation or attitude of a rigid body compared to a reference frame, we need to first consider a frame attached to the rigid body, then go about describing how the body-fixed frame is related to the inertial frame. Basic concepts first in 2D, then in 3D. The direction cosine matrix [C], sometimes abbreviated as the DCM, relates the frames (the triad of unit vectors) but also vectors in each frame. We discuss the direction cosine matrix on its own, before we discuss how to describe it in terms of 3 Euler angles in a later lecture, for example, yaw, pitch, and roll.
► Next: Euler Angles for Aerospace | Yaw, Pitch, Roll
https://youtu.be/SrLcvAw1iW4
► Previous, Rigid System of Particles | From Discrete Particles to the Continuous Limit of an Extended Mass Distribution
https://youtu.be/nMNWu4ZX340
► More lectures posted regularly
Be informed, subscribe https://is.gd/RossLabSubscribe
► Dr. Shane Ross, aerospace engineering professor, Virginia Tech
Background: Caltech PhD | worked at NASA/JPL & Boeing
Research website for @ProfessorRoss
http://shaneross.com
► Follow me on Twitter
https://twitter.com/RossDynamicsLab
► Lecture notes (PDF)
https://is.gd/SpaceVehicleDynamicsNotes
► All course videos (playlist)
https://is.gd/SpaceVehicleDynamics
► Reference:
Schaub & Junkins, Analytical Mechanics of Space Systems, 4th edition, 2018
https://arc.aiaa.org/doi/book/10.2514/4.105210
► Topics covered in course https://is.gd/SpaceVehicleDynamics
- Typical reference frames in spacecraft dynamics
- Mission analysis basics: satellite geometry
- Kinematics of a single particle: rotating reference frames, transport theorem
- Dynamics of a single particle
- Multiparticle systems: kinematics and dynamics, definition of center of mass (c.o.m.)
- Multiparticle systems: motion decomposed into translational motion of c.o.m. and motion relative to the c.o.m.
- Multiparticle systems: imposing rigidity implies only motion relative to c.o.m. is rotation
- Rigid body: continuous mass systems and mass moments (total mass, c.o.m., moment of inertia tensor/matrix)
- Rigid body kinematics in 3D (rotation matrix and Euler angles)
- Rigid body dynamics; Newton's law for the translational motion and Euler’s rigid-body equations for the rotational motion
- Solving the Euler rotational differential equations of motion analytically in special cases
- Constants of motion: quantities conserved during motion, e.g., energy, momentum
- Visualization of a system’s motion
- Solving for motion computationally
#RigidBodyKinematics #RotationMatrix #Rotation #RigidBody #Kinematics #DirectionCosineMatrix #Rigidity #InertiaMatrix #MomentOfInertia #InertiaTensor #EngineeringDynamics #SystemOfParticles #ConservationOfEnergy #WorkedProblem #WorkedExample #Dumbbell #CenterOfMass #MatlabTutorial #Tutorial #Lecture #Matlab #NewtonsLaws #ConservationOfMomentum #SolutionStrategy #ProblemSolving #ProblemSolvingStrategy #TransportTheorem #RotatingFrame #InertialFrame #VectorDerivative #SatelliteGeometry #RotatingFrames #SpacecraftDynamics #SpaceVehicle #AttitudeDynamics #SpaceVehicleDynamics #RigidBodyDynamics #dynamics #LawsOfMotion #engineering #aerospace #ElonMusk #spacetravel #SpaceX #Boeing #Satellite #Satellites #SpaceDomainAwareness #NewtonsLaw #NewtonsLawofMotion #EquationOfMotion #Newtons2ndLaw #NewtonianMechanics #AOE3144 #Caltech #NASA #VirginiaTech #engineering #dynamics #mechanics #physics #mathematics #science #aerospace #mechanicalengineering #spacecraft #openaccess #OnlineCourse #technology #robotics #space #spaceindustry #math #biomechanics #vehicledynamics #simulation #aerodynamics #innovation #NewtonEuler #SingleDegreeofFreedom #LinearMotion #NonlinearDynamics #DynamicalSystems #AppliedMath #ChaosTheory #Bifurcation #DifferentialEquations #mathematics #Newton #math #FreeCourses #OnlineCourse #Lagrangianpoints #Lyapunov #VectorField #GraphicalMethod #FixedPoints #EquilibriumPoints #NonlinearODEs #StablePoint #UnstablePoint #Stability #LinearStability #StabilityAnalysis #VectorField #Pendulum #Poincare #mathematicians #maths #mathstudents #mathematician #mathfacts #mathskills #mathtricks