Contact Geometry Between a Wheelset and Track. 2nd Report, Three Dimensional Contact Geometry for Measured Worn Profiles.

Contact Geometry

2 Contact manifolds 4 2.1 Contact manifolds and their submanifolds . . . . . . . . . . . . . . 6 2.2 Gray stability and the Moser trick . . . . . . . . . . . . . . . . . . 13 2.3 Contact Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Darboux’s theorem and neighbourhood theorems . . . . . . . . . . 17 2.4.1 Darboux’s theorem . . . . . . . . . . . . . . . . . . . . . . . 17...

Modeling of heat generations for different tool profiles in friction stir welding: study of tool geometry and contact conditions

In this work, improved heat generation models are developed for straight and tapered shoulder geometries with different tool pin profiles in friction stir welding. The models are developed considering the welding process as a combination of the pure sliding and the pure sticking conditions. From the results, the amount of heat generation is directly proportional to the number of edges in the pi...

Contact Geometry of One Dimensional Holomorphic Foliations

ABSTRACT. Let V be a real hypersurface of class Ck, k ≥ 3, in a complex manifold M of complex dimension n + 1, HT (V ) the holomorphic tangent bundle to V giving the induced CR structure on V . Let θ be a contact form for (V,HT (V )), ξ0 the Reeb vector field determined by θ and assume that ξ0 is of class Ck. In this paper we prove the following theorem (cf. Theorem 4.1): if the integral curves...

3-dimensional Methods in Contact Geometry

Contact Geometry of Curves

Cartan’s method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group G. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers the complete set of invariant data which solves the G-equivalence problem via a straightforward procedure, and which is, in some sense a supplement to the equi...