University of Colorado Boulder - Spacecraft Relative Motion Kinematics and Kinetics

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Spacecraft Relative Motion Kinematics and Kinetics
at
Coursera
Overview

Gain a comprehensive introduction to the principles and techniques used to analyze and control the relative motion of spacecraft

Duration	33 hours
Start from	Start Now
Total fee	Free
Mode of learning	Online
Difficulty level	Advanced
Official Website	Explore Free Course
Credential	Certificate

Spacecraft Relative Motion Kinematics and Kinetics
at
Coursera
Highlights

Earn a certificate of completion
Financial aid facility available
Projects and assignments for better preparation

Spacecraft Relative Motion Kinematics and Kinetics
at
Coursera
Course details

Who should do this course?

Aerospace Engineering Students

Space Science and Engineering Professionals

Researchers in Space Dynamics and Astrodynamics

What are the course deliverables?

Describe relative motion with a range of coordinates

Understand standard relative orbit prototypes

Assess the impact of perturbations on the relative motion

Setup bounded relative orbits for a range of chief eccentricities

More about this course

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

Spacecraft Relative Motion Kinematics and Kinetics
at
Coursera
Curriculum

Revisiting Basics of Keplerian Motion

Welcome to the Course!

Newtons Law

Vector Algebra

Example of Using Transport Theorem

Review of Vector Algebra

Kepler's Laws

Conic Section Properties

Review of Orbit Geometries

Orbit Differential Equations of Motion

Orbital Angular Momentum

Eccentricity Vector

Orbit Energy

Review: Fundamental Integrals

Kepler's Equation

Review: Kepler's Equation

Coordinate Transformations

Supplemental Material

Supplemental Material: Basic Astrodynamics Information

Quiz 1 – Newtons Law

Quiz 2 – Vector Algebra

Quiz 3 – Kepler's Laws

Quiz 4 – Conic Section Properties

Quiz 5 – Orbit Differential Equations of Motion

Quiz 6 – Orbital Angular Momentum

Quiz 7 – Eccentricity Vector

Quiz 8 – Orbit Energy

Quiz 9 – Fundamental Integrals & Kepler's Equation

Quiz 10 – Coordinate Transformations

Variation of Parameters

Lagrangian Matrix

Example: Spring-Mass System

Review of General Variation of Parameters

Lagrange Brackets

Example: Non-Conservative Variational equations with Lagrangian Coeffient Matrix

Lagrange's Planetary Equations

Example: J2 Perturbed Variational Equations

Poisson Brackets

Example: Classic Orbit Element Variational Equations

Review of Poisson Brackets

Gauss' Variational Equations

Gauss' Variational Equations in Velocity Frame

Quiz 1 – Lagrange Matrix

Quiz 2 – Lagrangian Brackets

Quiz 3 – Lagrange's Planetary Equations

Quiz 4 – Poisson Brackets

Quiz 5 – Gauss' Variational Equations

Spacecraft Formation Flying

Introduction to Formation Flying

Review Orbit Mission Scenarios and Definitions

Relative Motion Nomenclature

Mapping Betweeen LVLH and Inertial Frames

Review: LVLH-Inertial Mapping

General Relative Equations of Motion

Linearized General Relative EoM

Review: Relative Equations of Motion

CWH Equations

Review: CWH Equations

CW Equations with Curvilinear Coordinates

Tschauner-Hempel Equations

Closed Form CWH Solutions

Examples: Relative Orbit Illustrations

Review: CWH Trajectories

Perturbed Chief Frame Angular Velocity

Review: Perturbed Orbit Frame

Relative Orbits with Orbit Element Differences

Review: Relative Trajectories with OE Differences

Linear Mapping Between Differential Orbit Elements and LVLH Coordinates

Review: Linear Mapping Matrix [A]

Inverse of [A] Mapping Matrix

Variational Math

Relative Orbit Barycenter

Example: Barycenter on Circular Orbits

Linearized Differential Mean Anomaly Solution

Review: Variation of Differential Mean Anomaly

Linearized OE-Difference Solution

Non-Dimensional Linearized OE-Difference Solution

Small Eccentricity OE-Difference Solutions

Velocity Frame OE-Difference Solution

Example: 3D Relative Orbits Illustrations with Eccentric Chief

OE-Difference Solution with Mean J2 Perturbation

Example: Numerical Comparison of OE-Solutions

Quiz 1 – Basics of Formation Flying

Quiz 2 – Formation Flying Nomenclature

Quiz 3 – Relative Motion Mapping

Quiz 4 – General Relative Equations of Motion

Quiz 5 – Linearized General Relative EOM

Quiz 6 – CWH Equations

Quiz 7 – Curvilinear CWH

Quiz 8 – TS Equation

Quiz 9 – CWH Solutions

Quiz 10 – Perturbed Chief Orbit Angular Velocity

Quiz 11 – OE Difference Relative Orbit Descriptions

Quiz 12 – Linear Mapping between OE Differences and LVLH Coordinates

Quiz 13 – Variational Math

Quiz 14 – Formation Barycenter

Quiz 15 – Linearized Differential Mean Anomaly

Quiz 16 – OE Difference Solutions

Quiz 17 – OE-Difference Solutions Considering J2

Bounded Relative Motion

Introduction to Bounded Relative Orbits

Bounded Linearized Relative Motion with Circular Chief

Bounded Linearized Relative Motion with Elliptic Chief

Impact of J2 Perturbation on Inertial Motion

J2-Invariant Relative Orbit Constraints

Review: J2-Invariant Orbit Conditions

Orbit Energy of J2-Invariant Relative Orbits

Numerical Examples of J2-Invariant Relative Orbits

Near Polar Challenges with J2-Invariant Relative Orbits

Near Circular Chief Orbit Challenges with J2-Invariant Relative Orbits

Predicting ∂? = -∂M Drift

Correcting ?? = -?M Drift

Fuel Usage for General Mean Element Differences

Quiz 1 – Bounded Relative Motion with Circular

Quiz 2 – Bounded Relative Motion with Elliptic Chief

Quiz 3 – Inertial J2 Perturbation

Quiz 4 – J2 Invariant Relative Orbits

Quiz 5 – Orbit Energies of J2-Invariant Solutions

Quiz 6 – Numerical Solution to J2-Invariant Relative Orbit

Quiz 7 – NearPolar J2-Invariant Relative Motion

Quiz 8 – Near-Circular Case of J2-Invariant Relative Orbits

Quiz 9 – ?? = -?M Drift with J2-Invariant Orbits

Quiz 10 – Correcting ?? = -?M Drift

Quiz 11 – Fuel Usage Predictions

Spacecraft Relative Motion Kinematics and Kinetics
at
Coursera
Faculty details

Hanspeter Schaub

Dr. Schaub is the Glenn L. Murphy Chair in Engineering at the University of Colorado. He has over 25 years of research experience, of which 4 years are at Sandia National Laboratories. His research interests are in nonlinear dynamics and control, astrodynamics, relative motion dynamics, as well as relative motion sensing.