Appendix 1

State Space Format

We have seen in Section 5.2 that the simplest way to describe handling of a vehicle with linear tire characteristics, under action of external force F_ye, moment M_ze, and/or steering angle input δ, is by using the following equations:

$m \cdot V \cdot (\overset{\cdot}{β} + r) = Y_{β} \cdot β + Y_{r} \cdot r + C_{α 1} \cdot δ + F_{y e}$ (A1.1)

(A1.1)

$J_{z} \cdot \overset{\cdot}{r} = N_{β} \cdot β + N_{r} \cdot r + a \cdot C_{α 1} \cdot δ + M_{z e}$ (A1.2)

(A1.2)

where the derivatives of stability Y_β, Y_r, N_β, and N_r are defined by (see also Section 5.2):

$Y_{β} = - (C_{α 1} + C_{α 2})$ (A1.3)

(A1.3)

$Y_{r} = - \frac{a \cdot C_{α 1} - b \cdot C_{α 2}}{V}$ (A1.4)

(A1.4)

$N_{β} = - (a \cdot C_{α 1} - b \cdot C_{α 2})$ (A1.5)

(A1.5)

$N_{r} = - a$

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Essentials of Vehicle Dynamics by Joop Pauwelussen

State Space Format

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