The kinematics of particles and rigid bodies in the plane are investigated up to higher-order accelerations. Discussion of point trajectories leads from higher-order poles to higher-order Bresse circles of the moving plane. Symplectic geometry in vector space R^2 is used here as a new approach and leads to some new recursive vector formulas.
In this article biarc geometry is examined from a purely geometric point of view.
Two given points together with their associated tangent vectors in the plane are sufficient to define two directed, consecutive circular arcs. However, there remains one degree of freedom to determine the join point of both arcs. There are various approaches to this in the literature. A novel one is presented here.
This is a reprint of my original online article with the same title from Feb. 2007. I did not change anything except Markdown related formatting and a few typos. The original inline links are moved to a reference section. Some of them are dead links and marked (†). The reason for republishing is the announcement of JSONPath as an Official Internet Protocol Standard (RFC 9535) 17 years later based on that original article having a size of 6 print pages. I recommend to read Glyn Normington's blog post for some more insight to the spec and historical notes. This success would not have been possible without the professional editorial work of Glyn, Carsten, Tim and others. Thanks go to them.
yes ... V.I.Arnold - important symplectic geometry author tells us: "Hamilton mechanics cannot be understood without differential forms ...". Thanks for your link.
