Multibody systems are among the most important models in engineering design and analysis. An efficient analysis of multibody system dynamics requires both a reliable and fast formalism for the automatic generation of the equations of motion and an appropriate numerical integration algorithm and software. Initial value problems for multibody systems are a very special class of problems with a variety of properties that present a challenge to a numerical analyst: The governing equations and the way they are evaluated depend on the problem formulation as well as the formalism applied. Since dimensions may be high, strategies for minimizing the amount of work spent on matrix calculations are required. Discontinuities and nondifferentiabilities from phenomena like impact, back-lash, Coulomb friction, stick-slip, and hysteresis models have to be dealt with. The equations of motion are delivered by a formalism typically on a set of differential-algebraic equations which has index 3.
In author’s monograph recently developed tools for the numerical integration of multibody systems are presented and discussed in detail. A multistep approach with an orthogonal projection method onto invariant manifolds prove to be convergent with the same order as the original method. The solution not only satisfies the constraints more accurately, but is even more accurate, in general. In order to overcome discontinuities, a switching procedure with a special driver algorithm for the numerical integrator has been realized. By means of practical examples the applicability, reliability, and efficiency of the methods developed is demonstrated.
The clear written and well organized monograph will be of interest to all concerned with dynamics.