Abstract
This chapter lays down the fundamental representation concepts that will be used in the book thereafter. It eventually defines the concept of a “von Mises motor”, which is a compound vector including force and moment vectors. This compound representation of forces and moments in turn defines a geometric space/representation, where all the balance laws are going to be formulated upon. It continues by laying the basic theorems that will be used to formulate the Cosserat continuum, together with the appropriate kinematic fields conjugate to the “motor” vectors that are naturally called “kinematic von Mises motors”. Such a kinematic motor is a compound vector including linear velocity and spin (angular velocity), fully describing a rigid body motion in the new reduced geometric representation.
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- 1.
In German literature this is called Dyname, a term that stems from the Greek word δύναμις; in French literature it is called torseur.
- 2.
German: Stab.
- 3.
This section is mostly inspired by the presentation of the subject, given by my Teacher, late Professor Bitsakos (Γεωργικόπουλος Κ.Χ. και Μπιτσάκος Λ.Ι., Τεχνική Μηχανική Β’, Γραφοστατική, Εκδ. Τεχνικού Επιμελητηρίου της Ελλάδος, 1967.).
- 4.
This is true because two force-couples can be added by adding their moments.
- 5.
Δύναμις, Greek for dynamic action.
- 6.
Note that in a rigorous but heavy presentation, in the expressions for the vector products one should use the point vector \( \varvec{f} \) instead of the free vector \( \varvec{F} \).
- 7.
The selection of the reduction point is arbitrary. However a general rule must be put down if one wants to produce some useful result.
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Vardoulakis, I. (2019). Rigid-Body Mechanics and Motors. In: Cosserat Continuum Mechanics . Lecture Notes in Applied and Computational Mechanics, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-319-95156-0_2
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