Related papers: A rational Rodrigues' formula to interpolate rotat…
As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the…
We derive and simulate a mathematical model for mechanotransduction related to the Rho GTPase signalling pathway. The model addresses the bidirectional coupling between signalling processes and cell mechanics. A numerical method based on…
Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…
We analyze a mathematical model that describes the interaction between an insulating rigid body and an incompressible electrically conducting fluid surrounding it. The model as well as the mathematical analysis involve the fields of…
This paper provides the mathematical expressions, formulated in classical trigonometric terms, that are required (i) to compute an animal's body orientations and rotations in 3D space from data acquired at high-frequency by on-board…
The metohod of ortogonal rotations introduced in the previous papers of the author is used for construction of the explicit form the generators of the simple roots for quantum (and ussual) semisimple algebras. All calculations are presented…
Rigid body with rotors is a widespread mechanical system modeled after the direct product $SO(3)\times S^1\times S^1\times S^1$, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and…
A framework for performing event-driven, adaptive time step simulations of systems of rigid bodies interacting under stepped or terraced potentials in which the potential energy is only allowed to have discrete values is outlined. The…
Physical reasoning is a core aspect of intelligence in animals and humans. A central question is what model should be used as a basis for reasoning. Existing work considered models ranging from intuitive physics and physical simulators to…
We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…
We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk…
RodFIter is a promising method of attitude reconstruction from inertial measurements based on the functional iterative integration of Rodrigues vector. The Rodrigues vector is used to encode the attitude in place of the popular rotation…
We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.
A mechanical model was developed to describe the behaviour of a device able to transform vibrations into rotations, named Vibrot. The theoretical model, developed in the newtonian formulation of mechanics, was able to reproduce…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational…
The goal of the first part of this note is to get an explicit formula for rotation number and Mather $\beta$-function for ellipse. This is done here with the help of non-standard generating function of billiard problem. In this way the…
In this article, we plan to provide an introduction about some basics about robots for readers. Several key topics of classic robotics will be introduced, including robot representation, robot rotational motion, coordinates transformation…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
The purpose of this paper is to make clear the difference between rigid and undeformable bodies in Relativity. The error of confusing these two concepts has survived up to the present day treatises. We hope it will not persist in the XXI…