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SD2910 Spacecraft Dynamics 9.0 credits

This course covers the attitude control of rigid spacecraft. The rotational kinematics in three dimensions is fully covered with Direction Cosine Matrix, Euler angles, Principal rotation vector, Euler parameters, Classical Rodrigues parameters and Modified Rodrigues parameters. A few static attitude determination methods are introduced. The dynamic behaviour axi-symmetric and asymmetric rigid bodies under both external torques, e.g. constant torque and gravity gradient torque, and with no torque are covered. Lyapunov stability theory is used to develop stabilizing nonlinear control laws and linearization of the equations of motion is used to determine gain parameters for both regulation and tracking problems.

About course offering

For course offering

Spring 2025 Start 17 Mar 2025 programme students

Target group

Open for: TAEEM, TTEMM, TSUEM och TIPUM, THCIM, TTFYM, TMLEM, TERGM and CDEPR, CFATE, CMAST, CMATD, CTFYS year 3 as long as it can be included in your program.

Part of programme

Master's Programme, Aerospace Engineering, åk 1, Optional

Master's Programme, Aerospace Engineering, åk 1, FLT, Optional

Master's Programme, Aerospace Engineering, åk 1, RMD, Mandatory


P4 (9.0 hp)


17 Mar 2025
2 Jun 2025

Pace of study


Form of study

Normal Daytime

Language of instruction


Course location

KTH Campus

Number of places

Places are not limited

Planned modular schedule


For course offering

Spring 2025 Start 17 Mar 2025 programme students

Application code



For course offering

Spring 2025 Start 17 Mar 2025 programme students


Gunnar Tibert (


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Course coordinator

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Headings with content from the Course syllabus SD2910 (Spring 2022–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Part 1: Rigid body kinematics parameterizations in three dimensions: Direction cosine matrix, Euler angles, principal rotation vector, Euler parameters (quaternions), classical and modified Rodrigues parameters.

Part 2: Rigid body dynamics: angular momentum, kinetic energy and moment of inertia in three dimensions, Euler’s rotational equations of motion, torque-free rigid body rotation, dual-spin spacecraft, momentum exchange devices and gravity gradient stabilization.

Part 3: Nonlinear spacecraft stability and control: stability definitions, Lyapunov stability, Lyapunov functions, nonlinear feedback control laws, Lyapunov optimal control laws and linear closed-loop dynamics.

Intended learning outcomes

After completing course the student should be able to:

  1. Demonstrate broad knowledge and understanding for the scientific basis and proven experience in attitude control of spacecraft, as well as insight into current research and development work.
  2. Demonstrate basic methodology and understanding of attitude control of spacecraft, including three-dimensional rotational kinematics, rigid body dynamics and non-linear regulation.
  3. Demonstrate the ability to critically and systematically integrate knowledge from previous courses to analyse, assess and deal with complex phenomena, problems and situations within attitude control of spacecraft, even with limited information.
  4. Demonstrate the ability to model, simulate, predict and evaluate the rotational motion and stability of spacecraft as well as their passive and active attitude control, even with limited information.
  5. Demonstrate ability to clearly present and discuss engineering conclusions and the knowledge and arguments behind them, in dialogue with different groups, orally and in writing, in international contexts.

For the higher grades, the student should also be able to

       6. Demonstrate in-depth methodology and understanding of attitude  control of spacecraft, including three-dimensional kinematics, rigid body dynamics and non-linear regulation.

Literature and preparations

Specific prerequisites

Completed degree project on Bachelor level with major in technology.

English B / English 6

Recommended prerequisites

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Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F


  • PRO1 - Assignments with Oral Presentation, 4.0 credits, grading scale: A, B, C, D, E, FX, F
  • TEN1 - Oral Examination, 5.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

The participants are required to complete the following:

  • Four problem sheets, related to the four parts of the course. The problem sheets are released at given dates and have to be submitted for correction before given deadlines.
  • Oral presentation of selected problem sheet problems in front of class. The presenting students are randomly selected.
  • Oral examination on all four parts of the course.  

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

Mechanical Engineering

Education cycle

Second cycle

Add-on studies

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Gunnar Tibert (