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Euler's Equations of Rigid Body Dynamics Derived | Qualitative Analysis | Build Rigid Body Intuition

Space Vehicle Dynamics 🤓 Lecture 21: Rigid body dynamics, the Newton-Euler approach, is given. Specifically, from the angular momentum rate equation, we derive the most common forms of Euler's equations of the rotational dynamics of a rigid body. A qualitative analysis of Euler's equation is also given to build intuition. ► Next: Free rigid body motion | precession of axisymmetric bodies | general motion    • Free Rigid Body Motion | Precession o...   ► Previous, Center of Mass & Moment of Inertia Matrix | Example Calculations    • Center of Mass & Moment of Inertia Ma...   ► 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 ► Follow me on Twitter   / rossdynamicslab   ► Space Vehicle Dynamics course videos (playlist) https://is.gd/SpaceVehicleDynamics ► Lecture notes (PDF) https://is.gd/SpaceVehicleDynamicsNotes ► References Schaub & Junkins📘Analytical Mechanics of Space Systems, 4th edition, 2018 https://arc.aiaa.org/doi/book/10.2514... ► Related Courses and Series Playlists by Dr. Ross 📚Space Vehicle Dynamics https://is.gd/SpaceVehicleDynamics 📚3-Body Problem Orbital Dynamics Course https://is.gd/3BodyProblem 📚Space Manifolds https://is.gd/SpaceManifolds 📚Lagrangian and 3D Rigid Body Dynamics https://is.gd/AnalyticalDynamics 📚Nonlinear Dynamics and Chaos https://is.gd/NonlinearDynamics 📚Hamiltonian Dynamics https://is.gd/AdvancedDynamics 📚Center Manifolds, Normal Forms, and Bifurcations https://is.gd/CenterManifolds ► Chapters 0:00 Summary so far 0:37 Newton-Euler approach to rigid bodies 10:22 Qualitative analysis to build intuition about rigid bodies 11:06 Spinning top analysis 15:36 Spinning bicycle wheel on string 19:06 Fidget spinner analysis 22:01 Landing gear retraction analysis 24:53 Euler's equations of rigid body motion derived in body-fixed frame 29:09 Euler's equation written in components 30:56 Euler's equation in principal axis frame 35:33 Euler's equation for free rigid body 40:32 Simulations of free rigid body motion ► 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 #RigidBodyDynamics #EulersEquation #Gyroscope #SpinningTop #EulersEquations #RigidBody #FreeRigidBody #Axisymmetric #Prolate #Oblate #MomentOfInertia #CenterOfMass #InertiaMatrix #InertiaTensor #AttitudeDetermination #AttitudeEstimation #SpacecraftAttitudeControl #Spacecraft #SpacecraftOrientation #TRIAD #TRIADmethod #ADCS #MATLAB #MATLABdemo #MATLABtutorial #Numerics #NumericalDemonstration #EulerAngles #AngularVelocity #RigidBodyKinematics #AxisAngle #Quaternions #EulerParameters #RotationAxis #RodriguesFormula #RotationMatrix #RigidBody #YawPitchRoll #Rotation #BryanTait #aircraft #spacecraft #TaitBryan #Kinematics #DirectionCosineMatrix #Rigidity #EngineeringDynamics #SystemOfParticles #ConservationOfEnergy #WorkedProblem #WorkedExample #CenterOfMass #MatlabTutorial #Tutorial #Lecture #Matlab #NewtonsLaws #ConservationOfMomentum #TransportTheorem #RotatingFrame #InertialFrame #VectorDerivative #SatelliteGeometry #RotatingFrames #SpacecraftDynamics #SpaceVehicle #AttitudeDynamics #SpaceVehicleDynamics #RigidBodyDynamics #dynamics #LawsOfMotion #engineering #aerospace #elonmusk #SpaceX #Boeing #Satellite #Satellites #SpaceDomainAwareness #NewtonsLaw #EquationOfMotion #Newtons2ndLaw #NewtonianMechanics #AOE3144 #Caltech #NASA #VirginiaTech #engineering #dynamics #mechanics #physics #mathematics #science #aerospace #mechanicalengineering #spacecraft #openaccess #OnlineCourse #technology #robotics #space #spaceindustry #math #vehicledynamics #simulation #NewtonEuler #LinearMotion #NonlinearDynamics #DynamicalSystems #AppliedMath #DifferentialEquations #mathematics #Newton #math #FreeCourses #OnlineCourse #EquilibriumPoints #StablePoint #UnstablePoint #maths #mathematician