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Vehicle system dynamics

Instructor: Antonio Carcaterra
Course web page: Vehicle System Dynamics at DIMA
Credits: 6
Infostud code: 1041431


A twofold approach is proposed. On one hand the vehicle is decomposed into sub-systems: (i) propulsion (ii) transmission (iii) thrust and directional components (iv) suspension systems (v) brake systems (vi) guidance and control. On the other hand a general model of the vehicle integrating the considered sub-systems is developed, which is able to predict the different maneuvering ability of the vehicle.
The theoretical foundation to approach vehicle dynamics is provided. The objective of this course is twofold: on one hand, the student is provided with the most advanced techniques of analysis in the field of vehicle's dynamics; on the other hand, the student is guided in applying these tools to the design of real devices and in the implementation of these concepts in computer programs.



  1. Introduction to vehicle dynamics
  2. General modelling and control of the vehicle system
    • The vehicle sub-system architecture: body, propulsion system, transmission, devices for attitude and thrust control of the vehicle, suspensions, sensors, actuators
    • General equations of the vehicle plant and its controls
    • Hamilton’s principle and Euler-Lagrange approach
    • Linear and nonlinear models, models by linearization, stability
    • Special models of sub-systems for design purposes
    • Control basics, feedback control of vehicle sub-systems
    • PID controllers
    • Optimal problems based on Hamilton’s principle
    • Pontryagin’s theory of optimal control, LQR-LQG
  3. Kinematics and dynamics of tyres
    • Kinematics of a rolling deformable wheel
    • Brush Model and its advances
    • Brush-Rod-Beam Model
    • General Eulerian model of a deformable tyre in contact with a rigid road
    • Combined effects of longitudinal and lateral slip
    • Lagrangian models
    • Semi-empirical models - Pacejka
    • Unsteady dynamics of the rolling tyre: wave propagation effects and critical rolling speed
    • The tyre as a dynamic device for steering and thrusting/braking (analogy with propellers and rudders)
  4. Propulsion plant, transmission and their coupling
    • General characteristics and modelling of the internal combustion engines and electric motors/generators
    • Transmission types: traditional gear transmission, robotic actuators, automatic (epicyclic); CVT (continuous variable transmission): belt, hydraulic, electromechanical power splitters, pure electromagnetic, transmission plant for hybrid vehicles, Torotrak, gyroscopic-transmission
    • Basic performance of the transmission
    • Selection of the gear ratios in traditional transmission
    • Selection of the CVT control
    • Modelling of a transmission plant
    • General control of a transmission plant
  5. Vibrations and suspensions
    • A general theory of suspensions: comfort and handling
    • Vibration sources
    • Analysis of a quarter-car: implication for stiffness and damping values
    • General architecture of the suspension system and its degrees of freedom
    • Geometry of different used solutions
    • Roll analysis
    • Kinematic roll centre
    • Static roll centre
    • Roll dynamics and rollover
    • Pumping and pitch analysis
    • Comfort: design principles (coincident pitch-heave natural frequencies)
    • Handling: anti-dive and anti-squat
    • Special suspensions: pneumatic, hydro-pneumatic, mixed, interconnected
    • Theory and design of semi-active damping control (Skyhook and recent advances)
  6. Dynamic models
    • General dynamics of the vehicle
    • Special dynamic models: pump-pitch, roll, forward-yaw
  7. Special vehicles


  1. Longitudinal dynamics
    • Acceleration of the vehicle with conventional transmission
    • Acceleration of the vehicle with CVT and controllers
    • Controlled braking of a vehicle
  2. Vehicle steering
    • Kinematic steering
    • Dynamic steering: tires, roll, suspensions
    • Stability
  3. Controlled sub-systems
    • Controlled smart suspensions
    • ABS, ESP and other semi-active and active controllers

Type of exam: Oral test, Project

Reference texts

  • Antonio Carcaterra, “Notes on Vehicle System Dynamics”, 2018
  • Massimo Guiggiani, "Dinamica del Veicolo", Città Studi, 2007
  • Giancarlo Genta, "Meccanica dell'Autoveicolo", Levrotto & Bella, 2000
  • Hans B. Pacejka, “Tyre and Vehicle Dynamics”, Butterworth-Heinemann, 2002