Essentials of Vehicle Dynamics

Appendix 2

System Dynamics

A2.1 General Approach in N Dimensions

Consider the n-dimensional autonomous ordinary differential equation

$\underset{\_}{\stackrel{·}{x}}=\underset{\_}{F}(\underset{\_}{x};\underset{\_}{u})t>0$ (A2.1)

(A2.1)

where $\underset{\_}{x}$ is an n-dimensional function in time and $\underset{\_}{u}$ is an m-dimensional time-dependent input, i.e.,

$\underset{\_}{x}:[o,\infty )\to I{R}^n\underset{\_}{u}:[o,\infty )\to I{R}^m$

Likewise, the right-hand side function $\underset{\_}{F}$ =(F₁, F₂, …, F_n)^T will ...