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Spacecraft Relative Motion Kinematics and Kinetics · LearnSpace
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Spacecraft Relative Motion Kinematics and Kinetics

Курс от University of Colorado Boulder
Продвинутый≈ 33.3 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

Spacecraft relative motion control has many applications including rendezvous and docking, circumnavigation, on orbit assembly, servicing, etc. The course Spacecraft Relative Motion Kinematics and Kinetics covers the fundamentals of describing the motion of one spacecraft as seen by another spacecraft. A range of relative coordinates are investigated. Further, the course covers developing the differential equations of motion of the relative motion and considers a range of assumptions on separation distances. Finally, the impact of the J2 perturbation on the relative motion is studied. After this course, you will be able to... * Describe relative motion using rectilinear or curvilinear Hill frame coordinates, using relative orbit elements, as well as using differential orbit elements. * Develop the differential equations of relative motion for both near circular and highly elliptical chief motions * Predict the impact of perturbations on the relative motion * Understand how to setup relative orbits that remain bounded to the chief. Please note: this is an advanced course, best suited for working engineers or students with college-level knowledge in mathematics and physics. The material covered is taking from the book "Analytical Mechanics of Space Systems" available at https://arc.aiaa.org/doi/book/10.2514/4.105210.

Навыки, которые вы освоите

Differential EquationsApplied MathematicsLinear AlgebraPhysicsMathematical ModelingMechanicsTrigonometryControl SystemsCalculusAdvanced Mathematics

Программа курса

4 модулей · 121 учебных материалов

01Revisiting Basics of Keplerian Motion29 материалов

Introduction to Spacecraft Relative Motion Kinematics and Kinetics

Course Updates and Accessibility SupportЧтениеWelcome to the Course!Видео

Particle Kinematics Fundamentals

Supplemental MaterialЧтениеNewtons Law Видео

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Hanspeter Schaub

Glenn L. Murphy Chair in Engineering, Professor

Spacecraft Relative Motion Kinematics and Kinetics
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Обучение на Coursera

≈ 33.3 ч

4 модулей

Язык: Английский

Часть программы вашего университета
Quiz 1 – Newtons LawЗадание
Vector Algebra Видео
Example of Using Transport TheoremВидео
Review of Vector AlgebraВидео
Quiz 2 – Vector AlgebraЗадание

Keplerian Motion

Supplemental Material: Basic Astrodynamics InformationЧтениеKepler's LawsВидеоQuiz 3 – Kepler's LawsЗаданиеConic Section PropertiesВидеоReview of Orbit GeometriesВидеоQuiz 4 – Conic Section Properties ЗаданиеOrbit Differential Equations of MotionВидеоQuiz 5 – Orbit Differential Equations of MotionЗаданиеOrbital Angular MomentumВидеоQuiz 6 – Orbital Angular MomentumЗаданиеEccentricity VectorВидеоQuiz 7 – Eccentricity VectorЗаданиеOrbit EnergyВидеоQuiz 8 – Orbit EnergyЗаданиеReview: Fundamental IntegralsВидеоKepler's EquationВидеоReview: Kepler's EquationВидеоQuiz 9 – Fundamental Integrals & Kepler's EquationЗаданиеCoordinate Transformations ВидеоQuiz 10 – Coordinate Transformations Задание
02Variation of Parameters17 материалов

Lagrange Brackets

Lagrangian MatrixВидеоExample: Spring-Mass SystemВидеоReview of General Variation of ParametersВидеоQuiz 1 – Lagrange MatrixЗаданиеLagrange BracketsВидеоExample: Non-Conservative Variational equations with Lagrangian Coeffient MatrixВидеоQuiz 2 – Lagrangian BracketsЗаданиеLagrange's Planetary EquationsВидеоExample: J2 Perturbed Variational EquationsВидеоQuiz 3 – Lagrange's Planetary EquationsЗадание

Poisson Brackets

Poisson BracketsВидеоExample: Classic Orbit Element Variational EquationsВидеоReview of Poisson BracketsВидеоQuiz 4 – Poisson BracketsЗаданиеGauss' Variational EquationsВидеоGauss' Variational Equations in Velocity FrameВидео
03Spacecraft Formation Flying51 материалов

Relative Orbit Examples

Introduction to Formation FlyingВидеоReview Orbit Mission Scenarios and DefinitionsВидеоQuiz 1 – Basics of Formation FlyingЗадание

Differential Relative Orbit Equations

Relative Motion NomenclatureВидеоQuiz 2 – Formation Flying NomenclatureЗаданиеMapping Betweeen LVLH and Inertial FramesВидеоReview: LVLH-Inertial MappingВидеоQuiz 3 – Relative Motion MappingЗаданиеGeneral Relative Equations of MotionВидеоQuiz 4 – General Relative Equations of MotionЗаданиеLinearized General Relative EoMВидеоReview: Relative Equations of MotionВидеоQuiz 5 – Linearized General Relative EOMЗаданиеCWH EquationsВидеоReview: CWH EquationsВидеоQuiz 6 – CWH EquationsЗаданиеCW Equations with Curvilinear CoordinatesВидеоQuiz 7 – Curvilinear CWHЗаданиеTschauner-Hempel EquationsВидеоQuiz 8 – TS EquationЗадание

Relative Orbit Solutions

Closed Form CWH SolutionsВидеоExamples: Relative Orbit IllustrationsВидеоReview: CWH TrajectoriesВидеоQuiz 9 – CWH SolutionsЗаданиеPerturbed Chief Frame Angular VelocityВидеоReview: Perturbed Orbit FrameВидео
04Bounded Relative Motion24 материалов

Bounded Relative Orbits Assuming Keplerian Motion

Introduction to Bounded Relative OrbitsВидеоBounded Linearized Relative Motion with Circular ChiefВидеоQuiz 1 – Bounded Relative Motion with CircularЗаданиеBounded Linearized Relative Motion with Elliptic ChiefВидеоQuiz 2 – Bounded Relative Motion with Elliptic ChiefЗадание

J2-Invariant Relative Orbits

Impact of J2 Perturbation on Inertial MotionВидеоQuiz 3 – Inertial J2 PerturbationЗаданиеJ2-Invariant Relative Orbit ConstraintsВидеоReview: J2-Invariant Orbit ConditionsВидеоQuiz 4 – J2 Invariant Relative OrbitsЗаданиеOrbit Energy of J2-Invariant Relative OrbitsВидеоQuiz 5 – Orbit Energies of J2-Invariant SolutionsЗаданиеNumerical Examples of J2-Invariant Relative OrbitsВидеоQuiz 6 – Numerical Solution to J2-Invariant Relative OrbitЗаданиеNear Polar Challenges with J2-Invariant Relative OrbitsВидеоQuiz 7 – NearPolar J2-Invariant Relative MotionЗаданиеNear Circular Chief Orbit Challenges with J2-Invariant Relative OrbitsВидеоQuiz 8 – Near-Circular Case of J2-Invariant Relative OrbitsЗадание

Fuel Cost Predictions due to Compensating for J2 Induced Drift

Predicting ∂ω = -∂M DriftВидео Quiz 9 – ∆ω = -∆M Drift with J2-Invariant OrbitsЗаданиеCorrecting Δω = -ΔM DriftВидеоQuiz 10 – Correcting ∆ω = -∆M DriftЗаданиеFuel Usage for General Mean Element DifferencesВидеоQuiz 11 – Fuel Usage PredictionsЗадание
Quiz 5 – Gauss' Variational EquationsЗадание
Quiz 10 – Perturbed Chief Orbit Angular VelocityЗадание
Relative Orbits with Orbit Element DifferencesВидео
Review: Relative Trajectories with OE DifferencesВидео
Quiz 11 – OE Difference Relative Orbit DescriptionsЗадание
Linear Mapping Between Differential Orbit Elements and LVLH CoordinatesВидео
Review: Linear Mapping Matrix [A]Видео
Inverse of [A] Mapping MatrixВидео
Quiz 12 – Linear Mapping between OE Differences and LVLH CoordinatesЗадание
Variational MathВидео
Quiz 13 – Variational MathЗадание
Relative Orbit BarycenterВидео
Example: Barycenter on Circular OrbitsВидео
Quiz 14 – Formation BarycenterЗадание
Linearized Differential Mean Anomaly SolutionВидео
Review: Variation of Differential Mean AnomalyВидео
Quiz 15 – Linearized Differential Mean AnomalyЗадание
Linearized OE-Difference SolutionВидео
Non-Dimensional Linearized OE-Difference SolutionВидео
Small Eccentricity OE-Difference SolutionsВидео
Velocity Frame OE-Difference SolutionВидео
Example: 3D Relative Orbits Illustrations with Eccentric ChiefВидео
Quiz 16 – OE Difference SolutionsЗадание
OE-Difference Solution with Mean J2 PerturbationВидео
Example: Numerical Comparison of OE-SolutionsВидео
Quiz 17 – OE-Difference Solutions Considering J2Задание