Towards an Object-oriented Implementation of VON MISES’ Motor Calculus Using Modelica

Abstract

This paper deals with a first implementation of the socalled motor calculus within Modelica. The motor calculus can be used to describe the dynamical behaviour of spatial multibody systems in an efficient way. This method represents an alternative approach to modelling of multibody systems. In the paper, some fundamentals of motor calculus are summarized. Furthermore, a simple implementation of motor algebra by special additional Modelica code within some components of the Modelica Multibody Standard Library is presented. This approach fully corresponds with the paradigm of object-oriented modelling. However, the present realisation is not equation-based in its full sense because of the missing possibility of operator overloading (at least in the available Modelica simulator environment). Instead of this, some functions are used carrying out the necessary calculations. Using this implementation, some examples are given to prove the applicability and correctness of the implemented approach.

Performance Analysis of VON MISES’ Motor Calculus within Modelica

“…Two of the examples can also be found in [15] where the authors already showed the applicability and correctness of some of the implementations. The following first three subsections describe the chosen examples and show some simulation results.…”

“…Hence, all motors can be seen as abstract objects that do not depend on the choice of a reference frame. Details can be found in [7,15].…”

“…For details we refer to [7,15]. In [15], it is also shown that, due to the definition of addition and scalar multiplication, motors span a vector space over the field of real numbers. Additionally, by the introduction of the outer product, motors form a Lie-Algebra 1 .…”

“…In our first publication [15], we were already able to show the possible simplifications of the resulting equations within some components of the Modelica Multibody Standard Library using the motor calculus. Furthermore, we compared both approaches e. g. with respect to numerical correctness.…”