About this online course


The Image

Course video

Building on the principles developed by Lagrange and Hamilton, in this course you will learn different methods to apply advanced dynamics principles to real-world project, where you need to assess how complex systems behave with regards to the kinetic and potential energy involved.

You will learn how to derive equations of motions for complex systems in a consistent and systematic way. There is no specific application area, however the course will include examples of aircraft, helicopters, satellites, wind turbines and robots. However the knowledge gained can be applied to any field of engineering which requires an understanding of analytical mechanics.

The course presents an efficient and systematic formulation of equations of motion for complex 3D dynamic systems in an innovative, easily assimilated format. It is intended for advanced graduate research and professional work. The advantage of this approach is that classic mistakes are avoided while the equations of motion for complex multibody dynamic systems are derived. The benefits for you are:

  • Improving your skills of modeling and deriving the equations of motion for complex 3D dynamic systems.
  • Setting up simulations to represent the motion of complex dynamic systems.

This makes this an ideal course for anyone who is working in simulation environments, robotics, aerospace, mechatronics, mechanical and biomedical applications. The course suits aerospace, mechanical and civil engineers, researchers or students for whom understanding theory of analytical mechanics and applying it (using MATLAB, Mathematica, Maple or any other programming language) will contribute to their work tasks or level of expertise.


"Nothing is particularly hard if you divide it into small jobs" (Henry Ford)

Rather like solving a tough mystery, this course is a "Howdunit" - tracking down and applying the equations of motion for complex dynamic systems. The course presents mechanics in a matrix from relation so that you can derive systematically in a short timeframe the equations of motion of complex systems.

The course begins with concepts that are simple and intuitive and then generalizes these concepts step by step into a broader analysis of the dynamics. The main goal of the course is to help you learn how to apply the fundamentals of Lagrangian mechanics to practical engineering problems. In this way you will learn to resolve intriguing problems in areas of engineering such as mechanical, aerospace, robotics, biomechanical, mechatronics.

The topics that are covered in this course are:

  • introduction to 3D mechanics appropriate for symbolic manipulation
  • matrix notation for vectors, vector transformation and vector multiplications, transformation matrix, rotation operator, inertia matrix
  • Momentum and Angular Momentum
  • kinetic energy of bodies with a fixed point in space
  • equations of motion of bodies with a fixed point in space (3D)
  • equations of motion of free bodies
  • Gyroscopic Motion
  • Hamilton's Principle
  • Lagrange equations
  • simulations using Lagrange equations of motion
  • alternative methods to derive equations of motion
Literature and Study Materials

Th. Van Holten "Advanced Dynamics", AE4-314 Lecture Notes, Delft University of Technology, 2002 - will be provided via the Electronic Learning Environment.


You will complete three assignments during the course and one final assignment which involves a simulation of the dynamics of a complex mechanical system. These assignments will be handed in digitally through the Electronic Learning Environment.



If you successfully complete your online course you will be awarded with a TU Delft certificate. The final grade is composed of course assignments 40%; the final assignment 60%. This certificate will state that you were registered as a non-degree-seeking student at TU Delft and successfully completed the course.

If you decide that you would like to apply to the full Master's program in Aerospace Engineering, you will need to go through the admission process as a regular MSc student. If you are admitted, you can then request an exemption for this course that you completed as a non-degree-seeking student. The Board of Examiners will evaluate your request and will decide whether or not you are exempted.


General admission to this course

Required prior knowledge

  • A relevant BEng or BSc degree in a subject closely related to the content of the course or specialized program in question, such as aerospace engineering, aeronautical engineering, mechanical engineering, civil engineering or (applied) physics.
  • If you do not meet these requirements because you do not have a relevant Bachelor's degree but you have a Bachelor's degree from a reputable institution and you think you have sufficient knowledge and experience to complete the course, you are welcome to apply, stating your motivation and reasons for admission. The faculty of aerospace engineering will decide whether you will be admitted based on the information you have provided. Appeal against this decision is not possible.

Expected prior knowledge
In addition to the entry requirements mentioned above, prior knowledge of the topic is necessary in order to complete this course, as well as Newtonian Dynamics as taught in most BSc engineering courses. For admission purposes, TU Delft will not ask you for proof of this prior knowledge, but it is your responsibility to ensure that you have the sufficient knowledge, obtained through relevant work experience or prior education.

Expected Level of English
English is the language of instruction for this online course. If your working language is not English or you have not participated in an educational program in English in the past, please ensure that your level of proficiency is sufficient to follow the course. TU Delft recommends an English level equivalent to one of the following certificates (given as an indication only; the actual certificates are not required for the admission process):

  • TOEFL score 90+ (this is an internet-based test)
  • IELTS (academic version) overall Band score of at least 6.5
  • University of Cambridge: "Certificate of Proficiency in English" or "Certificate in Advanced English"

Admission process

In order to complete your admission process you will be asked to upload the following documents:

  • a CV which describes your educational and professional background
  • a copy of your passport or ID card (no driver's license)
  • a copy of relevant transcripts and diplomas


If you have any questions about this course or the TU Delft online learning environment, please do not hesitate to contact us by sending an email.

Enrollment period is over

  • Start date
    Future dates to be announced
  • Cost
    € 750
  • Course length
    7 weeks
  • Estimated effort
    6 - 8 hours per week
  • Course code

Related courses