# Dynamics and Optimal Control of Road Vehicles 0198825714, 9780198825715

Dynamics and Optimal Control of Road Vehicles uniquely offers a unified treatment of tyre, car and motorcycle dynamics,

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English Pages 480 [477] Year 2018

Prehistory
Darwinian steering
The differential
Birth of the motor car
Early engines
Early car industry
Early bicycles
Driven bicycles
Transition to the ordinary
The ordinary
Rise of the safety bicycle
Further developments
Powered two-wheeled vehicles
First steam-powered machine
First motorcycle
Production motorcycles
Tyres
The first tyre
Detachable tyres
Tyre developments
Topics in Mechanics
Background
Equations of motion
Inertial reference frame
Newton's equations
Properties of the inertia tensor
Generalized coordinates
Constraints
Kinetic energy
Potential energy
Lagrange's equations
Lagrange's equations in quasi-velocities
Conservation laws
Energy
Linear momentum
Angular momentum
Hamilton's equations
Legendre transform
Canonical equations
Poisson brackets
Frames, velocity, and acceleration
Equilibria, stability, and linearization
Time-reversal symmetry and dissipation
Chaplygin's sleigh
T-symmetry of the Chaplygin sleigh
Dynamics of a rolling ball
Ball on an incline
Ball on an inclined turntable
Rolling disc
Introduction
Rolling constraints
Angular momentum balance
Equilibrium solutions
Lagrange's equation
Rolling stability
Tyres
Background
Tyre forces and slips
Sliding velocities
Pure side slip
Pure longitudinal slip
Pure spin slip
Combined lateral and longitudinal slip
Combined lateral, longitudinal, and spin slip
Summary of analytical models
Pure slip
Combined slip
Behaviour in non-reference conditions
Effect of inflation pressure
Hydroplaning
Thermal effects
Side slip and spin slip
Transfer function relationships
Low-speed modelling
Precursory Vehicle Modelling
Background
Simple car model
Constant speed case
Accelerating and braking
Cornering
Timoshenko–Young bicycle
Introduction
Steering kinematics
Vehicle dynamics
Lagrange's equation
Linearized model
Lumped-mass bicycle
Equations of motion
Wheel shimmy
Simple case
A more realistic setup
Unicycle
The Whipple Bicycle
Background
Bicycle model
Model features
Linear in-plane dynamics
Linear out-of-plane dynamics
Intermediate variables
Equations of motion
Modal analysis
Gyroscopic influences
Control-theoretic implications
A feedback-system perspective
Model extensions
Acceleration
Frame flexibility
Pneumatic tyres
Ride Dynamics
Background
Design objectives
Single-wheel-station model
Invariant equation
Interpolation constraints
State-space analysis
Suspension optimization
In-plane vehicle model
Invariant equations
Mode shapes
Reconciliation with single-wheel-station model
Transfer functions
Interpolation constraints
Full-vehicle model
Invariant equations
Mode shapes
Reconciliation with single-wheel-station model
Transfer functions
Rigid-chassis model
Further analysis
Background
Vehicle trim
Longitudinal load transfer in cars and motorcycles
Squat, dive, and pitch
Roll trim in motorcycles
Three-dimensional curves
Ribbons
Euler angles
Vehicle Positioning
Car modelling
Tyre friction
Wheel torque distribution
Suspensions
Aerodynamic maps
Driver modelling
Motorcycle modelling
Tyre contact geometry
Side-slipping relaxed tyres
Structural flexibility
Rider
Aerodynamic forces
Suspensions
Power transmission
Motorcycle multibody model
Remarks on vibration modes
Optimal Control
Background
Fundamentals
Pontryagin minimum principle (PMP)
Unconstrained case
Boundary conditions
Constancy of the Hamiltonian
Bounded controls
Bounded states and controls
Dynamic programming
Dynamic programming recurrence formula
The Hamilton–Jacobi–Bellman equation
Singular arcs and bang–bang control
Example: Goddard's rocket
Example: braking wheel
Example: Fuller's problem
Regularization
Numerical methods for optimal control
Explicit simulation (time-marching)
Implicit simulation (collocation)
Indirect methods
Direct methods
KKT vs PMP
Mesh refinement
Example: track curvature reconstruction
Vehicular Optimal Control
Background
An illustrative example
Constant-incline case
Regenerative braking
Dissipative braking
Fuel-efficient driving
Formula One hybrid powertrain
Track model
Important three-dimensional influences
Powertrain
Vehicle model
Scaling
Non-smooth features
Regularization