# Describing the Motions of Spacecraft

Hanspeter Schaub

The movement of bodies in space (like spacecraft, satellites, and space stations) must be predicted and controlled with precision in order to ensure safety and efficacy. Kinematics is a field that develops descriptions and predictions of the motion of these bodies in 3D space. This course in Kinematics covers four major topic areas: an introduction to particle kinematics, a deep dive into rigid body kinematics in two parts (starting with classic descriptions of motion using the directional cosine matrix and Euler angles, and concluding with a review of modern descriptors like quaternions and Classical and Modified Rodrigues parameters). The course ends with a look at static attitude determination, using modern algorithms to predict and execute relative orientations of bodies in space.

The movement of bodies in space (like spacecraft, satellites, and space stations) must be predicted and controlled with precision in order to ensure safety and efficacy. Kinematics is a field that develops descriptions and predictions of the motion of these bodies in 3D space. This course in Kinematics covers four major topic areas: an introduction to particle kinematics, a deep dive into rigid body kinematics in two parts (starting with classic descriptions of motion using the directional cosine matrix and Euler angles, and concluding with a review of modern descriptors like quaternions and Classical and Modified Rodrigues parameters). The course ends with a look at static attitude determination, using modern algorithms to predict and execute relative orientations of bodies in space.

After this course, you will be able to...

* Differentiate a vector as seen by another rotating frame and derive frame dependent velocity and acceleration vectors

* Apply the Transport Theorem to solve kinematic particle problems and translate between various sets of attitude descriptions

* Add and subtract relative attitude descriptions and integrate those descriptions numerically to predict orientations over time

* Derive the fundamental attitude coordinate properties of rigid bodies and determine attitude from a series of heading measurements

Enroll now

## What's inside

### Syllabus

Introduction to Kinematics
This module covers particle kinematics. A special emphasis is placed on a frame-independent vectorial notation. The position velocity and acceleration of particles are derived using rotating frames utilizing the transport theorem.
Rigid Body Kinematics I
This module provides an overview of orientation descriptions of rigid bodies. The 3D heading is here described using either the direction cosine matrix (DCM) or the Euler angle sets. For each set the fundamental attitude addition and subtracts are discussed, as well as the differential kinematic equation which relates coordinate rates to the body angular velocity vector.
Rigid Body Kinematics II
This module covers modern attitude coordinate sets including Euler Parameters (quaternions), principal rotation parameters, Classical Rodrigues parameters, modified Rodrigues parameters, as well as stereographic orientation parameters. For each set the concepts of attitude addition and subtraction is developed, as well as mappings to other coordinate sets.
Static Attitude Determination
This module covers how to take an instantaneous set of observations (sun heading, magnetic field direction, star direction, etc.) and compute a corresponding 3D attitude measure. The attitude determination methods covered include the TRIAD method, Devenport's q-method, QUEST as well as OLAE. The benefits and computation challenges are reviewed for each algorithm.

## Good to know

Know what's good
, what to watch for
, and possible dealbreakers
Covers the fundamental principles of rigid body kinematics, a core area in aerospace engineering and astronautics
Taught by Hanspeter Schaub, a recognized expert in the field of spacecraft attitude determination and control
Emphasizes practical applications, equipping learners with skills used in the aerospace industry
Covers advanced topics like quaternions and Classical Rodrigues parameters, which are essential for modern attitude control systems
Requires a strong foundation in mathematics and physics, making it suitable for advanced learners
Utilizes a rotating frame approach, providing a deeper understanding of particle kinematics

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## Reviews summary

### Well-received course on spacecraft kinematics

Learners say the course on kinematics in spacecraft is largely positive. Students highly recommend this course, describing it as amazing, great, and engaging. They especially note the clear and well-organized lessons, the challenging but rewarding assignments, and the excellent professor. Many have commented that the course has provided them with a strong foundation in spacecraft kinematics and has helped them gain confidence in their abilities.
Assignments help apply learned concepts
"Great course, the teacher makes us want to continue, it's clear and concise."
"The assignments where you had to write your own code to determine the spacecraft attitudes were very useful for applying what you had learnt."
"Very nice course, on a very good level, to students or professionals alike."
Passionate and knowledgeable instructor
"Amazing and passionate teaching."
"Excellent professor, very useful content and very complete."
"I really liked this course, the professor is really good at both explaining and deeply knowing the subject"
Neatly explained concepts and well-organized assignments
"Concepts are neatly explained."
"Great engineering course. Got a lot of knowledge in a simple way."
"Assignments are precise and well organized."
Limited support from instructors and staff
"There is NO HELP from teachers/instructors in the discussion forums at all, you are left with the courtesy of other students."
"Another is that the course uses python to submit the numerical assignments, however the "correct" answers that the course uses for grading you come from matlab"
"For 1 there is 0 support for learners, there's no mentors to help you, if you get stuck you will have to dig though the discussion boards or search google for help."

## Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Kinematics: Describing the Motions of Spacecraft with these activities:
Organize Course Materials
Organize notes, assignments, quizzes, and exams to enhance your understanding of the course by allowing you to review and reinforce concepts regularly.
Show steps
• Create a system for organizing materials, such as folders or digital notebooks.
• Regularly review and update your organized materials.
Review Classical Mechanics
Review the fundamental concepts of classical mechanics, such as Newton's laws of motion and conservation of energy, to strengthen your foundation for this course.
Browse courses on Classical Mechanics
Show steps
• Revisit textbooks or online resources on classical mechanics.
• Solve practice problems related to particle kinematics, rigid body kinematics, and statics.
Solve Kinematics Problems
Sharpen your problem-solving skills in kinematics by completing practice drills that cover particle and rigid body motion.
Browse courses on Kinematics
Show steps
• Find practice problems from textbooks, online resources, or past exams.
• Solve the problems, checking your answers to identify areas for improvement.
Five other activities
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Show all eight activities
Explore Euler Angles and Quaternions
Enhance your understanding of Euler angles and quaternions, two commonly used representations for describing rigid body orientations, by following guided tutorials.
Browse courses on Euler Angles
Show steps
• Find online tutorials or video lectures on Euler angles and quaternions.
• Work through the tutorials, taking notes and practicing the concepts.
Review and Discuss Concepts
Engage with peers in study groups or discussion forums to review course concepts, exchange ideas, and clarify any doubts.
Show steps
• Join or create study groups.
• Actively participate in discussions, asking questions and sharing insights.
Develop a Cheat Sheet
Create a cheat sheet summarizing the key concepts, formulas, and equations covered in the course, providing a quick reference for easy recall.
Show steps
• Identify the most important concepts, formulas, and equations.
• Organize and present the information in a clear and concise manner.
Assist Fellow Students
Reinforce your own understanding by assisting other students with their queries or coursework, providing valuable explanations and guidance.
Show steps
• Join online forums or discussion boards.
• Actively respond to questions and offer explanations or solutions.
Participate in Online Contests
Challenge yourself and assess your progress by participating in online contests or hackathons that focus on kinematics concepts.
Browse courses on Kinematics
Show steps
• Identify relevant online contests or hackathons.
• Participate in the events, working individually or as part of a team.

## Career center

Learners who complete Kinematics: Describing the Motions of Spacecraft will develop knowledge and skills that may be useful to these careers:
Spacecraft Design Engineer
Spacecraft design engineers design, develop, and test spacecraft. This course in Kinematics: Describing the Motions of Spacecraft provides a comprehensive understanding of the kinematics of rigid bodies, including attitude determination and control. Spacecraft design engineers can utilize this knowledge to design spacecraft structures and systems that ensure stability, maneuverability, and precise motion control. This course offers valuable knowledge and skills for individuals aspiring to become spacecraft design engineers.
Avionics Engineer
Avionics engineers design, develop, test, and maintain the electronic systems used in aircraft, spacecraft, and other vehicles. This course in Kinematics: Describing the Motions of Spacecraft provides a solid foundation in the kinematics of rigid bodies, including attitude determination and control. Avionics engineers rely on a deep understanding of spacecraft motion to design and implement avionics systems that ensure stability, maneuverability, and safe operation. This course directly aligns with the requirements of this role by equipping students with the necessary knowledge and skills.
Flight Dynamics Engineer
Flight dynamics engineers analyze and predict the motion of aircraft and spacecraft. This course in Kinematics: Describing the Motions of Spacecraft offers a comprehensive exploration of the kinematics of rigid bodies, including attitude determination and control. By understanding the principles governing the motion of spacecraft, flight dynamics engineers can accurately predict trajectories, plan maneuvers, and ensure the safe and efficient operation of spacecraft missions. This course is highly relevant to the field of flight dynamics engineering and provides a strong foundation for success in this role.
Guidance, navigation, and control engineers design and develop systems to guide, navigate, and control vehicles, including aircraft, spacecraft, and missiles. This course in Kinematics: Describing the Motions of Spacecraft provides a deep understanding of the kinematics of rigid bodies, including attitude determination and control. By mastering these concepts, guidance, navigation, and control engineers can effectively design and implement systems that ensure precise and reliable motion control for various vehicles. This course is highly valuable for individuals pursuing a career in this field.
Control Systems Engineer
Control systems engineers design, develop, and maintain control systems for various applications, including spacecraft, aircraft, and industrial processes. A key aspect of control systems engineering is understanding the kinematics of the system being controlled. This course in Kinematics: Describing the Motions of Spacecraft provides a comprehensive understanding of the kinematics of rigid bodies. Control systems engineers can apply the knowledge gained from this course to model, analyze, and design control systems for spacecraft, ensuring precise and stable motion.
Mission Analyst
Mission analysts plan, design, and execute spacecraft missions. This course in Kinematics: Describing the Motions of Spacecraft provides a comprehensive understanding of the kinematics of rigid bodies, including attitude determination and control. By mastering these concepts, mission analysts can effectively plan and execute maneuvers, optimize trajectories, and ensure the success of spacecraft missions. This course offers valuable knowledge and skills for individuals aspiring to become mission analysts.
Satellite Communications Engineer
Satellite communications engineers design, develop, and maintain satellite communication systems. This course in Kinematics: Describing the Motions of Spacecraft provides a deep understanding of the kinematics of rigid bodies, including attitude determination and control. Satellite communications engineers can apply this knowledge to design and optimize satellite communication systems, ensuring reliable and efficient communication between satellites and ground stations. This course is highly valuable for individuals pursuing a career in satellite communications engineering.
Aerospace Engineer
Aerospace engineers design, develop, test, and oversee the production of aircraft, spacecraft, and related systems. This course in Kinematics: Describing the Motions of Spacecraft delves into predicting and controlling the movement of bodies in space with precision. This knowledge is fundamental to the design and operation of spacecraft and is highly relevant to the field of aerospace engineering. By understanding the kinematics of spacecraft, students can contribute to the advancement of space exploration and the development of innovative aerospace technologies.
Robotics Engineer
Robotics engineers design, build, and maintain robots. This course in Kinematics: Describing the Motions of Spacecraft provides a strong foundation in kinematics, including the study of rigid body motion and attitude determination. Robotics engineers can apply this knowledge to model and control the motion of robots, enabling them to perform complex tasks with precision. This course is highly relevant for individuals pursuing a career in robotics engineering, particularly in areas involving spacecraft robotics.
Astronomer
Astronomers study the universe's physical properties, stars, planets, galaxies, and cosmic microwave background radiation. They interpret astronomical data to understand the origin, evolution, and composition of the universe. One can leverage the knowledge gained from this course to build a foundation in the celestial mechanics, a branch of astronomy that studies the motion of celestial objects, which would prove useful for a career as an astronomer. The course's focus on kinematics and describing the motions of spacecraft is directly applicable to the field of astronomy, where understanding the movement of celestial bodies is crucial.
Propulsion Engineer
Propulsion engineers design, develop, and test propulsion systems for aircraft, spacecraft, and other vehicles. This course in Kinematics: Describing the Motions of Spacecraft covers the kinematics of rigid bodies, including attitude determination and control. Propulsion engineers can utilize this knowledge to understand how spacecraft motion is affected by propulsion systems and design propulsion systems that optimize spacecraft performance. This course provides a valuable foundation for individuals pursuing a career in propulsion engineering.
Mechanical Engineer
Mechanical engineers design, develop, and build mechanical systems, including those used in spacecraft. This course in Kinematics: Describing the Motions of Spacecraft delves into the kinematics of rigid bodies, covering topics such as attitude determination and control. Mechanical engineers working in the aerospace industry can leverage this knowledge to design spacecraft components and systems that ensure accurate and stable motion. By understanding the kinematics of spacecraft, mechanical engineers can contribute to the development of innovative spacecraft technologies and missions.
Astrophysicist
Astrophysicists explore the universe's physical properties, including the behavior, physical properties, and dynamic processes of celestial objects and astrophysical phenomena. This course in Kinematics: Describing the Motions of Spacecraft provides a foundational understanding of the kinematics of celestial bodies, a field directly applicable to astrophysics. By learning to describe and predict the motion of spacecraft, students can gain valuable insights into the movement of stars, planets, and other celestial objects, which is crucial for astrophysical research.
Systems Engineer
Systems engineers integrate complex systems, including spacecraft, aircraft, and other large-scale systems. This course in Kinematics: Describing the Motions of Spacecraft provides a solid foundation in kinematics, including the study of rigid body motion and attitude determination. Systems engineers can apply this knowledge to model, analyze, and design complex systems, ensuring their functionality, safety, and performance. This course may be useful for individuals interested in pursuing a career in systems engineering, particularly in the aerospace domain.
Operations Research Analyst
Operations research analysts use advanced analytical techniques to solve complex problems in various industries, including aerospace. This course in Kinematics: Describing the Motions of Spacecraft provides a foundation in kinematics, including the study of rigid body motion and attitude determination. Operations research analysts can apply this knowledge to model and analyze spacecraft trajectories, optimize mission planning, and develop strategies for efficient and safe space operations. This course may be useful for individuals interested in applying operations research techniques to the aerospace domain.

We've selected 12 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Kinematics: Describing the Motions of Spacecraft.
Comprehensive reference for spacecraft attitude determination and control. It covers the fundamentals of kinematics and provides an in-depth look at modern algorithms for attitude determination and control.
Comprehensive textbook on spacecraft dynamics and control. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for spacecraft control.
Comprehensive textbook on spacecraft dynamics and control. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for spacecraft control.
It commonly used textbook for courses related to Astrodynamics. It can be used to learn the fundamentals necessary to understand Kinematics.
Comprehensive textbook on the kinematics and dynamics of multi-body systems. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for multi-body system dynamics.
Comprehensive textbook on dynamics. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for dynamics.
Comprehensive textbook on mechanics of materials. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for mechanics of materials.
Comprehensive textbook on applied kinematics. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for applied kinematics.
Comprehensive textbook on classical mechanics. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for classical mechanics.
Comprehensive textbook on mechanics. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for mechanics.
Comprehensive textbook on applied mechanics. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for applied mechanics.
Comprehensive textbook on engineering mechanics. It covers the fundamentals of kinematics and provides an in-depth look at modern methods for engineering mechanics.

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