In this article we give first results on Stewart Gough Platforms with planar base and platform, whose singularity set for any orientation of the platform is a cylindrical surface with rulings parallel to a given fixed direction p in the space of translations. In this case the singularity set can easily be visualized as curve by choosing p as projection direction. Moreover the computation of sin...

This paper is concerned with the analysis of a singularity that can occur in threedimensional discontinuous feedback control systems. The singularity is the two-fold – a tangency of orbits to both sides of a switching manifold. Particular attention is placed on the Teixeira singularity, which previous literature suggests as a mechanism for dynamical transitions in this class of systems. We show...

0 Introduction We consider algebraic surfaces Y ⊂ IP3(C). A cusp (=singularity A2) on Y is a singularity near which the surface is given in local (analytic) coordinates x, y and z, centered at the singularity, by an equation xy − z = 0. This is an isolated quotient singularity C2/ZZ3. A set P1, ..., Pn of cusps on Y is called 3-divisible, if there is a cyclic global triple cover of Y branched p...

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic...

The Cosmic Censorship Conjecture (CCC)[1,2] states that the space-time singularity produced by gravitational collapse must be covered by the horizon. The CCC is yet one of the unresolved problem in General Relativity. In fact the conjecture has not yet any precise mathematical proof. However the singularity theorems as such do not state anything about the visibility of the singularity to an out...

We study a simple system of two hyperbolic semi-linear equations, inspired by the Einstein equations. The system, which was introduced in [1], is a model for singularity formation inside black holes. We show for a particular case of the equations that the system demonstrates a finite time blowup. The singularity that is formed is a null singularity. Then we show that in this particular case the...

We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both in light-cone gauge and covariantly. We also compute some tree and one loop amplitudes which exhibit interesting behavior near the singularity. Our results a...

This paper presents the Eclipse-II, a new six degree-offreedom parallel mechanism, which can be used as a basis for general motion simulators. The Eclipse-II is capable of x, y and z-axis translations and a, b and c-axis rotations. In particular, it has the advantage of enabling continuous 360-degree spinning of the platform. The computational procedures for forward and inverse kinematics of th...

A black hole is considered a gravitational one-dimensional point of singularity containing an infinite mass within an infinitely small space, and spacetime curves infinitely. Within this singularity all the laws of physics are no longer valid. The physical domains of the large macroscopic scale are described by general relativity and on the small microscopic scale by quantum effects. It is prop...

This paper presents the Eclipse-11, a new six degree-offreedom parallel mechanism, which can be used as a basis for general motion simulators. The Eclipse-I1 is capable of x, y and z-axis translations and a, b and c-axis rotations. In particular, it has the advantage of enabling continuous 360-degree spinning of the platform. The computational procedures for forward and inverse kinematics of th...