{"paper":{"title":"On the Construction of Generalised Bobillier Formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Mehmet Ali Gungor, Soley Ersoy, Tulay Erisir","submitted_at":"2015-03-05T12:10:51Z","abstract_excerpt":"In this study, we consider the generalized complex number system $C_{\\rm{p}} = \\left\\{ {x + iy\\;:\\;x,y \\in R,\\;{i^2} = {\\rm{p}} \\in R} \\right\\}$ corresponding to elliptical complex number, parabolic complex number and hyperbolic complex number systems for the special cases of ${\\rm{p}} < 0,\\;{\\rm{p}} = 0,\\;{\\rm{p}} > 0$, respectively. This system is used to derive Bobillier Formula in the generalized complex plane. In accordance with this purpose we obtain this formula by two different methods for one-parameter planar motion in ${C_{\\rm{p}}}$; the first method depends on using the geometrical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01616","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}