# Vehicle Simple Nonlinear 4DOF

Nonlinear bicycle model nonlinear with 4 degrees of freedom.

The code of this class can be found in VehicleSimpleNonlinear4DOF. It inherits methods from abstract class VehicleSimple. The complete list of class codes is in API.

## Contents

## Theory

The development of the equations of motion of this model can be found in TheoryVehicleSimple4DOF.

## Sintax

`dx = VehicleModel.Model(t,states,tspan)`

`dx = VehicleModel.MassMatrix(t,states,tspan)`

## Arguments

The following table describes the input arguments:

t | Time |

states | Model state variables: [XT YT PSI VT ALPHAT dPSI] |

tspan | Time span |

## Description

The center of gravity of the vehicle is located at the point \(T\). The front and rear axles are located at the points \(F\) and \(R\), respectively. The constant \(a\) measures the distance of point \(F\) to \(T\) and \(b\) the distance of point \(T\) to \(R\). The angles \(\alpha_F\) e \(\alpha_R\) are the front and rear slip angles, respectively. \(\alpha_T\) is the vehicle side slip angle and \(\psi\) is the vehicle yaw angle. \(\delta\) is the steering angle.