Related papers: Position Equations of a 3RPR Planar Manipulator
The goal of this paper is to explain, using a typical example, the distribution of the different assembly modes in the workspace and their effective role in the execution of trajectories. The singular and non-singular changes of assembly…
It is well known in Riemannian geometry that the metric components have the best regularity in harmonic coordinates. These can be used to characterize the most regular element in the isometry class of a rough Riemannian metric. In this…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
We consider integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of us, extends to…
A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators,…
This article presents a new variable actuation mechanism based on the 3-RPR parallel robot. This mechanismis an evolution of the NaVARo robot, a 3-RRR parallel robot, for which the second revolute joint of the threelegs is replaced by a…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…
We study non-relativistic conformal field theory on a flat space in the presence of a planar boundary. We compute correlation functions of primary operators and obtain the expression for the boundary conformal block. We also discuss the…
Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic waves. The polarimetric quantities that are invariant under…
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…
The modified theories of gravity, especially the $f(R)$ gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane symmetric solutions in the context of metric $f(R)$ gravity. We extend the work on…
We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs (x,x') of points in R^n which satisfy d(x,x')>=epsilon. We interpret this as two or three (depending on the parity of n)…
Motion planning in high-dimensional space is a challenging task. In order to perform dexterous manipulation in an unstructured environment, a robot with many degrees of freedom is usually necessary, which also complicates its motion…
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…
Parameter--elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev…
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…
We further develop the formalism for taking position-space cuts of eikonal diagrams introduced in [Phys.Rev.Lett. 114 (2015), no. 18 181602, arXiv:1410.5681]. These cuts are applied directly to the position-space representation of any such…
In this paper we provide a systematic discussion of how to incorporate orientation preserving symmetries into the treatment of Willmore surfaces via the loop group method. In this context we first develop a general treatment of Willmore…
For the planar four-vortex problem, we show that there are finitely many stationary configurations consisting of equilibria, rigidly translating configurations, relative equilibria (uniformly rotating configurations) and collapse…