Related papers: Kinematics on oblique axes
Recursive matrix relations for kinematics and dynamics of the Orthoglide parallel robot having three concurrent prismatic actuators are established in this paper. These are arranged according to the Cartesian coordinate system with fixed…
In a recent paper, Saxena et al. [1] developed the solutions of three generalized fractional kinetic equations in terms of Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized…
The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…
The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here we present new scalable MFS…
The pure traction problem of elasticity appears frequently in engineering applications, and its complexity stems from the fact that its solution is unique only up to (infinitesimal) rigid body motions. When finite elements are employed to…
We present new integral representations in two dimensions for the elastance problem in electrostatics and the mobility problem in Stokes flow. These representations lead to resonance-free Fredholm integral equations of the second kind and…
We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
This paper addresses the numerical computation of critical angles between two convex cones in finite-dimensional Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary…
We consider the system of a two ball automatic dynamic balancer attached to a rotating disc with nonconstant angular velocity. We directly compare the scenario of constant angular velocity with that when the acceleration of the rotor is…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…
Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for…
Examples of axially symmetric solutions to Einstein's field equations are given that exhibit anomalous "negative frame dragging" in the sense that zero angular momentum test particles acquire angular velocities in the opposite direction of…
To enhance the understanding of the behavior of active nematic, it is important to understand the behavior of topological defects. In this paper, we study the configuration of topological defects of a two-dimensional active nematic around a…
The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the…
In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution of the orthonormal frame and the Navier--Stokes equation, which is derived from a molecular-theory-based dynamical tensor…
Where a 2D problem of optimal profile in variable speed flow is resolved in a class of convex Bezier curves, using symbolic and numerical computations.
We present a complete analysis of the linearised dynamics of active solids with orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include the possibility of stable active…