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>> YOUR LINK HERE: ___ http://youtube.com/watch?v=RpavqEtXoXk
Space Vehicle Dynamics, Lecture 4: vector manipulation review, transport theorem for derivatives in a rotating frame and two worked examples. Extension to frames that are rotating and translating. • ► Next: Worked examples using transport theorem | kinematics with rotating frames • • Worked Examples Using Transport Theor... • ► Previous: Coordinate frames, rotating frames | transport theorem introduced | cylindrical, spherical frames • • Coordinate Frames, Rotating Frames | ... • ► 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 and Boeing • Research website for @ProfessorRoss • http://shaneross.com • ► Follow me on Twitter • / rossdynamicslab • ► Lecture notes (PDF) • https://is.gd/SpaceVehicleDynamicsNotes • ► All course videos (playlist) • https://is.gd/SpaceVehicleDynamics • ► Courses and Playlists by Dr. Ross • 📚Attitude Dynamics and Control • https://is.gd/SpaceVehicleDynamics • 📚Nonlinear Dynamics and Chaos • https://is.gd/NonlinearDynamics • 📚Hamiltonian Dynamics • https://is.gd/AdvancedDynamics • 📚Three-Body Problem Orbital Mechanics • https://is.gd/SpaceManifolds • 📚Lagrangian and 3D Rigid Body Dynamics • https://is.gd/AnalyticalDynamics • 📚Center Manifolds, Normal Forms, and Bifurcations • https://is.gd/CenterManifolds • Chapters • 0:00 Review of vector manipulations • 6:40 matrix way to write cross-product, and the tilde matrix • 10:41 Transport Theorem for vector derivatives (transport equation) • 16:04 Example using cannon seen in rotating frame • 19:29 Oscillatory motion seen in rotating frame • 22:51 Turntable worked example of vector derivative • 36:36 Example of transport theorem for rotating Earth • 55:26 Transport theorem for frames that are translating and rotating • ► Reference: • Schaub Junkins, Analytical Mechanics of Space Systems, 4th edition, 2018 • https://arc.aiaa.org/doi/book/10.2514... • ► Topics to be 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 • Other topics as time allows • • #TransportTheorem #RotatingFrame #InertialFrame #VectorDerivative #SatelliteGeometry #RotatingFrames #SpacecraftDynamics #SpaceVehicle #AttitudeDynamics #SpaceVehicleDynamics #RigidBodyDynamics #dynamics #NewtonsLaws #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 #KAMtori
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