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Simulation Algorithms in Vehicle System Dynamics

Model based simulation in vehicle system dynamics relies on advanced methods for model setup, robust and efficient numerical solution techniques and powerful simulation tools for industrial applications. Most frequently the mechanical components are described by rigid or flexible multi-body system models that interact with electrical, hydraulic and other system components [1, 2], see also [3] for a summary of recent developments and [4] for a comprehensive overview on methods and algorithms that are tailored to industrial simulation packages. The first systematic treatment of numerical problems and numerical methods in multi-body dynamics from the viewpoint of vehicle system dynamics is the monograph of Eich–Soellner and Führer [5], see also [6]. In its simplest form the equations of motion of a multi-body system are given by a non-linear second order system of ordinary differential equations (ODEs) of moderate dimension that may be solved numerically by standard methods. The structure of the model equations gets more complicated if the multi-body system has kinematically closed loops [7]. Multi-body system models of wheel suspensions may be considered as a typical example in road vehicle simulation. The complex kinematics is modelled by constraints, the resulting model equations form a second order differential-algebraic equation (DAE). Robust and efficient DAE time integration methods are the backbone of state-ofthe-art multi-body system simulation software. Another important issue in simulation is the handling of discrete controllers that are beyond the classical time continuous