Course program
Course Program – Vehicle System Dynamics
Part I – Fundamentals of Vehicle Dynamics
Introduction to ground vehicle dynamics.
Kinematics of the rigid body and fundamental formulations.
Dynamic equilibrium equations of the rigid body and Lagrangian formulation.
Simplified vehicle models: from the full Newton–Euler system to the bicycle model.
Degrees of freedom of the vehicle system and conditions for dynamic equilibrium.
Concept of screw axis and its application to vehicle systems.
Linearization of the equations of motion and modal analysis.
Modal and forced response of the suspension system and associated screw axes.
Dynamic definition of roll and pitch screw axes.
Part II – Tire Theory
Introduction to tire dynamics and future application scenarios.
Modeling of the deformable tire:
longitudinal slip in straight motion;
pure and combined lateral slip;
rolling resistance and elastic deformation;
self-aligning moment and its influence on vehicle stability.
Definition and analysis of the grip factor and the adhesion/sliding regions.
Wheel alignment angles (camber, toe-in, toe-out) and their effect on vehicle dynamics.
Synthesis of input–output relationships for tire models.
Part III – Decoupled Motion Analysis of the Vehicle
Sub-model decoupling and separate motion analysis.
Planar motion (yaw–sway): equations of motion, dynamic response, and stability.
Steady-state analysis: understeer and oversteer behavior.
Suspension system: kinematic and dynamic principles.
Roll motion: definition of the roll axis and response to lateral excitations.
Pitch–heave motion: dynamic modeling, load transfer, and anti-dive characteristics.
Longitudinal (headway) motion: traction models, aerodynamic resistances, and tire–road adhesion.
Complete assembly of the vehicle’s equations of motion.
Part IV – Vehicle Control Elements
General architecture of vehicle control systems.
Review of control theory and variational formulations.
Euler–Lagrange equations applied to dynamic control.
Introduction to the LQR (Linear Quadratic Regulator) approach for optimal control.
Comparison between optimal control and heuristic tuning techniques.
Application examples: vehicle stabilization and cruise control.
Part V – Virtual Laboratory and Software Tools
Introduction to MATLAB/Simulink/Simscape for vehicle dynamics modeling.
Development of numerical models of the vehicle and tire subsystems.
Simulation of dynamic scenarios: acceleration, braking, stability, and anti-dive effects.
Analysis and validation of simulation results.
Final workshop: Modeling Longitudinal Vehicle Dynamics with Simscape.
Complementary Activities
Practical workshop on modeling and simulation using MATLAB/Simulink/Simscape.
Optional educational visit to the Vallelunga Racetrack, focused on vehicle control systems and telemetry applications.
Prerequisites
To successfully attend the course, students are expected to have:
a solid background in rational mechanics and rigid body dynamics;
knowledge of mechanical vibrations and multi-degree-of-freedom dynamic models;
fundamental skills in mathematics and linear algebra (differential calculus, linear systems, ordinary differential equations);
basic understanding of automatic control (dynamic systems theory, stability, state-space models);
preliminary experience with MATLAB/Simulink programming.
These prerequisites are usually fulfilled within a Bachelor’s degree in Mechanical, or equivalent.
Books
Main Teaching Material
Lecture notes prepared by the instructor (Prof. Nicola Roveri), available on Google Classroom, including:
slides, handwritten notes, and illustrative materials;
MATLAB/Simulink/Simscape exercises and scripts shared during the course;
instructions for the written test and for compiling the simulation report.
Recommended Reference Books
M. Abe, Vehicle Handling Dynamics – Theory and Application, Butterworth–Heinemann.
H. B. Pacejka, Tire and Vehicle Dynamics, Elsevier.
G. Genta, The Automotive Chassis, Springer.
W. F. Milliken, D. L. Milliken, Race Car Vehicle Dynamics, SAE International.
K. Popp, W. Schiehlen, Ground Vehicle Dynamics, Springer.
T. I. Fossen, Guidance and Control of Ocean Vehicles, Wiley.
K. M. Lynch, F. C. Park, Modern Robotics: Mechanics, Planning, and Control, Cambridge University Press.
R. M. Murray, Z. Li, S. S. Sastry, A Mathematical Introduction to Robotic Manipulation, CRC Press.
Supplementary Material
MATLAB/Simulink/Simscape documentation provided during the virtual laboratory sessions.
Handouts and notes from seminars and workshops (e.g., Modeling Longitudinal Vehicle Dynamics with Simscape).
Frequency
Course attendance is not compulsory, but it is recommended.
Regular participation in lectures and guided computer-based exercises allows students to follow the development of the topics more effectively, to become familiar with the proposed modeling and simulation methods, and to gradually acquire the competences required for the final examination.
Exam mode
The assessment is divided into two complementary parts:
Written test (1–2 hours)
Includes 2–4 questions/exercises on course topics.
Typical questions may cover planar vehicle dynamics, tire theory (brush model, longitudinal/lateral slip, grip factor), steering kinematics and dynamics, pitch/roll dynamics, cornering stability, or suspension geometry design.
The use of a computer is allowed only for numerical computations in MATLAB, with prior authorization and under strict supervision.
Simulation report and oral presentation
Development of a virtual experiment in MATLAB/Simulink/Simscape, documented in a written report (minimum 5 pages) and accompanied by the developed code.
Critical analysis of results and discussion of design implications.
Delivery of a 15-minute video presentation, where the student illustrates the results in a format similar to a thesis defense (voice-over slides or recorded discussion).
Final grading
The final grade combines both parts:
the written test evaluates theoretical mastery and problem-solving skills;
the report and presentation assess practical competences, critical thinking, and communication skills.
Bibliography
Main Teaching Material
Lecture notes prepared by the instructor (Prof. Nicola Roveri), available on Google Classroom, including:
slides, handwritten notes, and illustrative materials;
MATLAB/Simulink/Simscape exercises and scripts shared during the course;
instructions for the written test and for compiling the simulation report.
Recommended Reference Books
M. Abe, Vehicle Handling Dynamics – Theory and Application, Butterworth–Heinemann.
H. B. Pacejka, Tire and Vehicle Dynamics, Elsevier.
G. Genta, The Automotive Chassis, Springer.
W. F. Milliken, D. L. Milliken, Race Car Vehicle Dynamics, SAE International.
K. Popp, W. Schiehlen, Ground Vehicle Dynamics, Springer.
T. I. Fossen, Guidance and Control of Ocean Vehicles, Wiley.
K. M. Lynch, F. C. Park, Modern Robotics: Mechanics, Planning, and Control, Cambridge University Press.
R. M. Murray, Z. Li, S. S. Sastry, A Mathematical Introduction to Robotic Manipulation, CRC Press.
Supplementary Material
MATLAB/Simulink/Simscape documentation provided during the virtual laboratory sessions.
Handouts and notes from seminars and workshops (e.g., Modeling Longitudinal Vehicle Dynamics with Simscape).
Lesson mode
The course is mainly delivered through frontal lectures, with explanations provided by the professor supported by multimedia presentations and blackboard derivations. Lectures combine theoretical and application-oriented content, complemented by numerical examples and references to real-world cases.
In addition, the course includes:
guided exercises using MATLAB/Simulink/Simscape, aimed at introducing students to vehicle dynamics modeling and simulation;
a dedicated hands-on workshop on software tools;
possible seminars or technical visits (e.g., Vallelunga racetrack) as complementary learning activities.
Attendance is not compulsory but recommended in order to facilitate learning and effective understanding of the course contents.
