Related papers: Comparison of Methods for Rotating a Point in $\ma…

A new method of root finding is formulated that uses a numerical iterative process involving three points. A given function y = f(x) whose roots are desired is fitted and approximated by a polynomial function of the form P(x)= a(x-b)^N that…

All quaternion methods for static attitude determination currently rely on either the spectral decomposition of a 4 x 4 matrix (q-Method) or finding the maximum eigenvalue of a 4th-order characteristic equation (QUEST). Using a spectral…

We propose a general method for deep learning based point cloud analysis, which is invariant to rotation on the inputs. Classical methods are vulnerable to rotation, as they usually take aligned point clouds as input. Principle Component…

This paper is devoted to the detailed analysis of three-dimensional motions in $\mathbb{R}^3$ with orthogonal directions switching at Poisson times and moving with constant speed $c>0$. The study of the random position at an arbitrary time…

Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…

Using elementary geometric tools, we apply essentially the same methods to derive expressions for the rotation angle of the swing plane of Foucault's pendulum and the rotation angle of the spin of a relativistic particle moving in a…

Usual mathematical method for creating trochoids is based on a solid rule that requires a pure rolling motion of a circle along another one. In this vision a trochoid defined as a traced path by an attached point (a non-conceptive issue) to…

The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the…

We are interested in the naive problem whether we can move a solid object in a solid box or not. We restrict move to rotation. In the case we can, the centre and the ``direction'' of rotation may be restricted. Simplifying, we consider…

This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…

The motion of three interacting point vortices in the plane can be thought of as the motion of three geometrical points endowed with a dynamics. This motion can therefore be re-formulated in terms of dynamically evolving geometric…

A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of…

This work presents a three-dimensional geometric resolution method to calculate the complete inverse kinematics of a 7-degree-of-freedom articulated arm, including the hand itself. The method is classified as an analytical method with…

We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers, which formulate the P3P problem by intersecting two conics and constructing a degenerate conic…

Distinction among nearby poses and among symmetries of an object is challenging. In this paper, we propose a unified, group-theoretic approach to tackle both. Different from existing works which directly predict absolute pose, our method…

We consider imaging of fast moving small objects in space, such as low earth orbit satellites, which are also rotating around a fixed axis. The imaging system consists of ground based, asynchronous sources of radiation and several passive…

The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…

We propose a new method for the extraction of Rotation Measure from spectral polarization data. The method is based on maximum likelihood analysis and takes into account the circular nature of the polarization data. The method is unbiased…

We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…

This paper presents a new algorithm to estimate absolute camera pose given an axis of the camera's rotation matrix. Current algorithms solve the problem via algebraic solutions on limited input domains. This paper shows that the problem can…