Addenda and Erratum to: Characteristic directions of closed planar motions

作者：Dathe Henning^*; Gezzi Riccardo

来源：ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 2014, 94(6): 551-554.

DOI：10.1002/zamm.201300230

• Steiner formula
• planar kinematics
• motion characterization

In a previous paper [2], some properties of closed planar motions were investigated. The focus was on three aspects: the area enclosed by the paths of points, the polar moment of inertia and the natural average of a path. These three mathematical objects were shown to be interrelated.
For reasons of completeness, we now add some historical references which relate the problem considered to that of mechanical integrators eg. polarplanimeter.
In this communication, we introduce a fourth related entity, which is analogous to the action in theoretical mechanics. The relationship of action to the entities discussed in our previous article is given by a spatial invariant.
Then, we add some properties of the double hinge, in order to clarify the example given in the previous paper. Finally, we correct a sign error which appeared in [2]. In the Appendix (see Supplementary Material, Wiley online library), we present a general construction for spatial invariants.

• 出版日期2014-6