Mechanics II 7.5 credits

Mekanik II
First cycle, F0008T
Course syllabus valid: Autumn 2020 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.

Syllabus established
The syllabus was established by the Department of Applied Physics and Mechanical Engineering 2007-02-28, and remains valid from autumn 2007.

Last revised
by HUL Niklas Letho 14 Feb 2020

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. Alternatively for the master programme in secondary education, teaching in the upper-secondary school; U0002P, U0021P, M0033M.

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.


After passing this course the student should:

1.    Knowledge and understanding

• Have knowledge of the conditions for body equilibrium in three dimensions.

• Be able to define and formulate basic concepts and laws within three-dimensional classical particle and rigid dynamics which include relative motion in rotating, coordinate systems, central-force motion, Newton`s laws, angular momentum, momentum equations, energy methods, moment of inertia tensor, euler angles, Euler equations for gyroscopic motion, steady precession with zero moment and kinetic energy.

• Understand the concept of inertia forces and explain when they occur.

•  Be able to explain systems undergoing damped and forced vibrations and have knowledge about resonance and its consequences.

• Have knowledge of analytical mechanics as an alternative method to Newton's laws and be able to explain concepts such as constraints, degrees of freedom, phase-space, generalized coordinates, generalized momentum, the Lagrange and Hamilton functions.


2. Skills and abilities


• Be able to determine equilibrium conditions of bodies in the three dimensions.

• Be able to apply Newton´s laws and the momentum equation on three dimensional motion of bodies.

• Be able to perform calculations in rotating reference systems.

• Be able to calculate dynamic forces rotating mechanical systems and how these can be reduced with balancing.

• Solve problems with central motion.

• Have demonstrated the ability to use Newton's laws, energy methods, angular momentum, moment of inertia tensors and Euler's equations for gyroscopic motion in problem solving.

• Be able to analyze systems undergoing damped, forced and coupled vibrations.

• Be able to solve problems using analytical mechanics as an alternative method to Newton's laws, including Euler-Lagrange and Hamiltonian mechanics.

• Have demonstrated ability to formulate mathematical models and solve a mor technically challenging dynamic problems, both through idealized analytical solutions and by using computer-based tools (eg Matlab) for numerical solution.

• Show proficiency in oral and/or written presentations.


3.  Assessment and reasoning

• Practise problem solving.

• With a scientific approach, be able to evaluate whether results and calculations are reasonable and link the results to applications in engineering.

• Understand the limitations of analytical models and determine when numerical methods are to be used.

• Get awareness of different applications of mechanics in science and technology.


Equilibrium in three dimensions
Oblique central impact
Kinematics and kinetics in three dimensions
Fixed-axis rotation
Relative motion and general motion
Parallel-plane motion
General equations of motion
Analytical mechanics: invariances, principle of least action conservation laws, Euler-Lagrange equations, Hamiltonian mechanics such as Hamilton's canonical equations and Hamilton's principle and Hamilton-Jacobi theory
Central-force motion
Oscillations: free, damped and forced
The inertia tensor
Euler`s equations for rigid body dynamics
Gyroscopic motion
Numerical solutions in analytical mechanics


Lectures, lessons and home exercises with presentation, compulsory laboratory work on for example balancing of rotors or dynamic bearing forces. Alternatively, if agreed between student and examiner, the laboratory exercise can be to develop (including laboratory instructions) a student lab that can be used in physics teaching.


Written examination at the end of the course. Approved laboratory work and home/computer assignments are required There can be alternative examination methods.


This course cannot be part of the degree together with the courses F0055T, Mechanics II Space.

Nils Almqvist

Transition terms
The course F0008T is equal to MTF112

Literature. Valid from Autumn 2018 Sp 1 (May change until 10 weeks before course start)
Valid from Spring 2017 sp3 (May change until 10 weeks before course start)
Meriam-Kraige: Engineering Mechanics, Dynamics, 8th ed. ISBN 978-1-119-04481-9. Additional course material posted in the course room in Canvas or is available on the internet.. Search for books at the library

Course offered by
Department of Engineering Sciences and Mathematics

CodeDescriptionGrade scaleHPStatusFrom periodTitle
0001Written exam6 U G VG 3 4 5 *6.00MandatoryA07
0002Laboratory work and Assignment reportU G#1.50MandatoryA07

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.