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6.3 CONTINUUM MECHANICS 115

comb actuator, and an anchor (which corresponds with a fixed suspension). Imple-
mentation first raises the question of differentiating between a global and local
coordinate system. Initially all considerations of an element are local. However,
the element can also be given global coordinates, which can be used to solve a
calculation of the operating point. Thus the correct values of the global coordinates
are set automatically, whereas the actual calculations generally take place using a
further set of variables that only give values relative to the operating point.
The model of the bending beam was developed on the basis of a mechanical
structural analysis. The equation for the beam takes the form:

F beam = M¨u + B˙u + Ku (6.32)

where F beam represents the vector of forces and moments at the beam, u represents
the vector of the translational and rotational degrees of freedom of the beam, M
represents the mass matrix, B the damping matrix and K the stiffness matrix. In
principle this follows the beams presented in [34] and in Section 6.3.2, although
NODAS is more interested in the global movement and not in the deformation
of a continuum. Furthermore, the local mass, damping and stiffness matrices are
formulated directly in the hardware description language, which may cause these
symbolic equations to explode in the event of more complex elements.
However, in many cases physical modelling, as used in the previous examples,
is not possible or would be associated with great expense. In such cases it is often
worthwhile to move to experimental modelling. In this approach an experiment
does not necessarily consist of measurements on a real system, but often consists
of field and continuum simulations, for example based upon finite elements. In
this manner, the simulation can be run in advance of manufacture by the use
of experimental models. Pure table models, such as for example in Romanowicz
et al. [350] or Swart et al. [394], are an example. However, these table models,
with their data list of identification pairs, can be represented by compression into
relatively simple equations. This is shown by Teegarten et al. [397], who also
supply a lovely example of the mixing of physical and experimental modelling
based upon a micromechanical gyroscope.

6.3 Continuum Mechanics

6.3.1 Introduction

The previous section dealt with multibody mechanics, the main characteristic of
which is the consideration of a collection of bodies connected together by joints
and suspensions. The validity of this abstraction depends upon the formulation
of the question. In particular, the bending of mechanical components is often not
an undesirable side-effect, but is essential to the functioning of the system. Now,
if the form of bending plays a significant role in the system behaviour then we