On the Non‐Abelian Motor Calculus

Abstract

Es wird eine nichtlineare Erweiterung der Motorrechnung untersucht. Dazu wird der Motor T(3) D SO(3) definiert und die zugehorige Lie-Algebra angegeben. Die nichtlinearen Formen der Gradienten-, Rotor-und Divergenz-Operatoren werden hergeleitet, und ein energetisches Produkt fur zueinander konjugierte GroJen wird definiert. A nonlinear (non-abelian) extension of the motor analysis is considered. The semi-direct product T(3) D SO(3) is introduced and the associated Lie algebra is given. Nonlinear generalisation of the grad-, rotand div-operators are presented. An energetic product for variables conjugate with respect to the energy is defined. D SO(3) -m. e. momopu daemcrr npucoeduHeHHarr afize6pa flu. Bbls~drrrn~rr nenuHelSnble 0 6 0 6 y e~u a onepamopos grad (zpadue~m) , rot (sparyenue) u div (dusepze~yurr) . Onpedefirremcrr s~epzemuvecuoe npou3sede~ue dnrr conpxmeHHbix omHocumenbHo 3~epzuu nepemeHnbix. Paccmampusaemcrr HenunelSnoe (~ea6enesoe) pacutupeme momopozo a~anu3a. Beodumc~ cemu-nprrmoe npowsedenue T(3)

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

“…Recent publications dealing with this subject can rarely be found (exept e.g. for [8,18]). In the context of the modelling language for heterogenous systems Modelica (see e.g.…”

Performance Analysis of VON MISES’ Motor Calculus within Modelica

“…[2,3,12]), he introduced the motor as a six-tuple of scalar quantities and developed a special algebra for these mathematical objects, called the motor calculus. Though his approach is not well known throughout all branches of mechanical engineering, in the field of robotics VON MISES' ideas were rediscovered during the last decades [1,5,10,11,13], since they seem to be well suited to investigate the behaviour of spatial multibody systems. However, in the context of the modelling language Modelica (see e.g.…”