Motorrechnung im <i>X</i><sub>1+3+3</sub>

Heinz, C.

doi:10.1002/zamm.19870671105

Cited by 4 publications

(2 citation statements)

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“…[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.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of VON MISES’ Motor Calculus within Modelica

Zaiczek

Enge-Rosenblatt

2009

Linköping Electronic Conference Proceedings

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This paper presents an alternative concept of modelling multibody systems within Modelica, the socalled motor calculus. This approach was introduced by R. VON MISES in 1924 and can be used to describe the dynamical behaviour of spatial multibody systems in a very efficient way. While the equations clearly take a very simple form in terms of motor algebra, the numerical efficiency is still an open question.In the paper, first some fundamentals of motor calculus are summarized. An experimental implementation of motor algebra is used to measure and analyse the numerical efficiency and performance regarding the simulation time of VON MISES' approach. Therefore, some components of the Modelica Multibody Standard Library were modified in order to compare both implementations. Finally, some examples are given to prove the applicability and correctness of the concept but also to serve as a basis for a discussion of the numerical performance. The chosen approach utilizes all object-oriented features provided by the modelling language. Besides, it gives reason for the present endeavours to introduce the possibility of operator overloading within Modelica.

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Section: Introductionmentioning

confidence: 99%

Performance Analysis of VON MISES’ Motor Calculus within Modelica

Zaiczek

Enge-Rosenblatt

2009

Linköping Electronic Conference Proceedings

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“…Recently HEINZ [6] has given the rules of motor calculus for polar continua in the metric space M 1 + 3 + 3 with 1 + 3 translational and 3 complex rotational dimensions.…”

Section: Introductionmentioning

confidence: 99%

On the Non‐Abelian Motor Calculus

Stumpf

Badur

1990

Z Angew Math Mech

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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)

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