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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
MMF062 - Vehicle dynamics
Syllabus adopted 2008-02-20 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

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0103 Project 4,5c Grading: TH   4,5c    
0203 Examination 3,0c Grading: TH   3,0c   16 Dec 2008 pm V,  15 Apr 2009 am V,  Contact examiner

In programs

MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR - Control specialization, Year 1 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR - Mechatronics specialization, Year 1 (elective)


Bitr professor Robert Thomson
Docent Mathias Lidberg  Responsible: Programansv M Decision date: 2008-09-22


MMF061   Theory of ground vehicles

Course evaluation:


For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

The student requires knowledge of:
Statics (forces and moments, free body diagrams)
Kinematics (linear and angular motions)
Kinetics (planar motion of rigid bodies)
Linear algebra (solution of matrix equations)
Differential Equations (Solution of ordinary differential equations)

Successful completion of a Candidate Degree in Mechanical Engineering guarantees the students preparation for the course.


The course aims to take the student's existing knowledge of basic mechanics and apply them to road vehicles. The motions of the vehicle's centre of gravity will be analyzed in three independent analyses: longitudinal dynamics, lateral dynamics, and vertical dynamics. The vehicle systems relevant for its response in these directions will be introduced and described using first order differential equations. The student will be able to apply the concepts in the course to develop computer models that can describe the performance of each vehicle system independently.

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

Describe the forces acting between the tire and the road during the operation of a vehicle
Develop the first order mathematical models describing the longitudinal, lateral, and vertical dynamics of a vehicle
Implement analytical models into computer programs to describe the motions of a vehicle
Synthesize virtual prototypes of vehicle dynamics systems
Communicate concepts relevant for the performance, handling, and ride of a vehicle


The course will begin with an introduction to the basic mathematical and mechanics concepts relevant for analyzing vehicle dynamics. The vehicle will be treated as a set of dynamic systems and detailed component analyses (ie kinematic analyses of suspension linkages) will not be undertaken. Four separate modules are used to describe the relevant systems and their analysis.

Mathematic and Mechanical Notations

Module 1: Tire
Tire forces/moments
Tire Construction / Tire Types
Rolling resistance
Longitudinal slip
Lateral slip
Combined slip
Simple tire models
Module 2: Longitudinal Dynamics (Acceleration/Braking Performance)
Wheel torque applied to road: Single tire car model
Braking and acceleration: 2 axle vehicle model (load shift)
Braking and acceleration: 2 axle vehicle model (load shift and vehicle pitch)

Module 3: Lateral Dynamics (Handling)
Low speed Ackermann Steering
Bicycle model
High speed steady state turning
Transient steering
Lateral load transfer
Stability analysis
Module 4: Vertical Dynamics (Ride)
Road roughness representation
Suspension components (springs and dampers)
1 and 2 Degree of freedom Quarter car model
Bounce Pitch Model


The course includes formal lectures, computer laboratories and tutorial sessions.


Extended lecture notes.


A final written examination will comprise 50% of the course grade. Submitted assignments in the course will make up the remainder of the grade.

Page manager Published: Thu 04 Feb 2021.