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Mechanics II Space 7.5 credits

Mekanik II Ry
First cycle, F0055T
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Education level
First cycle
Grade scale
G U 3 4 5
Subject group (SCB)
Main field of study
Engineering Physics and Electrical Engineering

Entry requirements

In order to meet the general entry requirements for first cycle studies you must have successfully completed upper secondary education and documented skills in English language and Basic mechanics corresponding to the courses Physics 1 and 3(F0004T and F0006T) Basic courses in calculus, algebra, analysis and ordinary differential equations corresponding to the courses M0029M, M0030M, M0031M, M0032M.

More information about English language requirements


The selection is based on 1-165 credits.

Course Aim
The content of the course is a continuation of the basic courses in mechanics and aims for students to further broaden and deepen their knowledge of classical mechanics, which also becomes a base for further studies in physics and space engineering such as for orbit and attitude dynamics. It also includes alternative methods within classical mechanics.

After passing this course the student can:

1.    Knowledge and understanding
  • describe and express  the conditions for body equilibrium in three dimensions.
  • account for concepts and explain basic concepts and laws within three-dimensional classical particle and rigid dynamics with significance for space engineering.
  • explain inertial forces and describe when they occur.
  • account for systems undergoing damped and forced vibrations, explain resonance and exemplify  its consequences such as for space rockets.
  • describe basic principles for propulsion of aircrafts and space rockets.
  • describe analytical mechanics as an alternative method to Newton's laws, can elucidate basic concepts and account for Lagrange's equations.
2.    Competence and skills
  • determine the conditions for force equilibrium of bodies in three dimensions.
  • solve problems with movement of bodies in three dimensions i.e. make calculations based on translating, accelerating and rotating coordinate systems, use Newton's laws, energy methods, momentum, inertial matrix, Euler's equations for gyroscopic motion and analyze damped, forced and coupled oscillations.
  • calculate dynamic forces in rotating mechanical systems due to dynamic imbalance.
  • solve problems with central-force motion, especially planet and satellite orbits.
  • solve dynamic problems for particles and rigid bodies using analytical mechanics:
            a)    formulate Lagrange function for different physical situations;     
            b)    derive the equations of motion and solve Euler-Lagrange's equations for mechanical systems with one or a few generalized
  • calculate mass flow and acceleration when propelling a rocket.
  • make a mechanical design to fulfill more complicated technical dynamics problems (vibration problems) by using simulations.
  • communicate model and simulation in a structured scientific report.

3. Judgement and approach
  • use a scientific approach to critically evaluate results, draw conclusions and argue for a chosen technical solution for space technology.

Equilibrium in three dimensions, trusses .
Oblique central impact.
Kinematics and kinetics in three dimensions: relative motion, motion relative accelerating, translating and rotating coordinates; central-force motion, especially planet and satellite orbits; Newton's laws; equations of motion; momentum; angular momentum; kinetic energy; angular-momentum equations; the inertia tensor; rotation about a fixed point; parallel-plane motion; dynamic imbalance; Rigid body kinematics parameterizations in three dimensions; principal rotation vector; Euler angles; introduction to Euler parameters and quaternions; Euler's equations for rigid bodies; gyroscopic motion with examples for attitude control; precession with zero moment; rotating and dual-spinning spacecraft; stability.

Vibrations: free, damped and forced vibrations in mechanical systems; satellites and vibrations.

Kinematics and kinetics of particle systems in applications with examples in rocket propulsion.

Analytical mechanics: force constraint; degrees of freedom; generalized coordinates; generalized momentum; invariances and conservation laws; the Lagrange function and Euler-Lagranges equations.

Dynamic modeling and mechanical design with computer aids (normally Comsol Multiphysics, alternatively Matlab).

Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.
The teaching consists of lectures and lessons. In order for the student to achieve the course objectives, the student is encouraged to participate in these learning activities, read the corresponding sections in the course literature and solve the proposed exercises. It is mandatory laboratory work on gyroscopic motion and hand-in assignments/computer assignments.

The assignment involves identifying a more technically advanced dynamic problem related to space engineering by using computer-based aids for mechanical design, visualization and simulation. Normally, this is analysis, development and optimization of a CubSat frame to fulfil given vibration criteria during launch.

If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.

It is normally a written examination with differentiated numerical grades at the end of the course. In addition, approved report of hand-in assignments and presentation of laboratory results, are required.


The course can not be a part of the degree together with F0008T Mechanics II.

Nils Almqvist

Literature. Valid from Autumn 2021 Sp 1 (May change until 10 weeks before course start)
Meriam-Kraige-Bolton: Engineering Mechanics, Dynamics, 9th edition (ISBN: 9781119665281) eller motsvarande.
Additional course material posted in the learning management system Canvas or is available on the internet.

Course offered by
Department of Engineering Sciences and Mathematics

CodeDescriptionGrade scaleCrStatusFrom periodTitle
0003Laboratory work and assignmentsU G#1.00MandatoryA21
0004Written examG U 3 4 56.50MandatoryA21

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established
by HUL Mats Näsström 14 Feb 2017

Last revised
by Head Faculty Programme Director Niklas Lehto 17 Feb 2021