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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
MMF062 - Vehicle dynamics
Syllabus adopted 2014-02-19 by Head of Programme (or corresponding)
Owner: MPAUT
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Automation and Mechatronics Engineering, Mechanical Engineering, Shipping and Marine Technology, Industrial Design Engineering
Department: 42 - APPLIED MECHANICS

Teaching language: English
Open for exchange students
Block schedule: D

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0103 Project 4,5 c Grading: TH   4,5 c    
0203 Examination 3,0 c Grading: TH   3,0 c   13 Jan 2015 pm M,  13 Apr 2015 pm M,  18 Aug 2015 am M

In programs



Professor  Bengt Jacobson


MMF061   Theory of ground vehicles

  Go to Course Homepage


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Statics (equilibrium, forces and moments, free body diagrams)
Kinematics and kinetics (linear and angular motions, mainly in one plane)
Dynamic systems, differential equations (basic level)
Linear algebra (matrix equations)
Stationary vibrations and step response in linear mekanical systems.
Successful completion of a Bachelor Degree in Mechanical Engineering guarantees the students preparation for the course.


The course aims to that the students should be able to apply their existing knowledge of basic mechanics on road vehicles. The motions of the vehicle body as a rigid body will be analysed separately in three directions: longitudinal, lateral and vertical. The vehicle sub-systems relevant for vehicle response in these directions will be briefly described in words and simple equations. The student will be able to apply the concepts in the course to solve simpler problems for complete vehicle dynamics; both by hand calculations and by developing and using computer models.

Learning outcomes (after completion of the course the student should be able to)

After the course the student should be able to:

  • Describe and calculate the forces acting between the tire and the road during the operation of a vehicle.
  • Describe design and basic function of the vehicle systems: propulsion, brake, steering and suspension.
  • Understand and do basic models of the mentioned vehicle systems, capturing such as: front/rear axle drive, anti-dive/anti-squat suspension, axle roll-centre, rack steering, roll-axis.
  • Compile the models of the vehicle systems to a vehicle level model, and use it to verify vehicle function requirements for manouvres that mainly are either of longitudinal, lateral and vertical.


The course will treat the vehicle as consisting of a set of sub-systems, of which detailed analyses (i.e. kinematic analyses of suspension linkages) will not be undertaken. The course (and compendium) is divided into five modules (chapters) as follows:

  • Module 1: Introduction: Introduction to the engineering task of vehicle dynamics engineers. Short recap of basic mathematical and mechanical engineering concepts relevant for analyzing vehicle dynamics.
  • Module 2: Vehicle interactions: Mainly tyre/road contact, including models for rolling resistance and longitudinal and lateral slip and forces. Briefly about combined longitudinal and lateral slip.
  • Module 3: Longitudinal Dynamics: Acceleration/Braking/Gradeability Performance. 2-axle vehicle model for longitudinal load shift. Briefly about anti-dive and anti-lift suspension.
  • Module 4: Lateral Dynamics: Low speed manouvering, Ackermann Steering, One-track model, High speed steady state turning, Handling diagram, Stability analysis, Stationary oscillating steering, Transient handling, Briefly about roll-axis and lateral load transfer. Briefly about manouvres on friction limit. Briefly about combined longitudinal and lateral dynamics.

  • Module 5: Vertical Dynamics: Ride comfort, Road grip on rough road, Road waviness model, Suspension components (springs and dampers), 1- and 2-Degree of freedom quarter car model, Bounce & Pitch Model. Briefly about non-stationary vertical dynamics.


  • Lectures
  • Problem solving sessions
  • Assignments


  • Compendium
  • Lecture presentation slides
  • Problems for problem solving including problems from old exams


  • Marked assigment reports (50%)
  • Graded written examination with problem solving (50%)

Page manager Published: Thu 04 Feb 2021.