On pseudohyperbolic space motions

Abstract

In the present paper, the geometrical instantaneous invariants of the motion H m /H f in dual Lorentzian 3 -space are determined. Depending on this, the dual Lorentzian instantaneous screw axis of the motion of K m with respect to the dual pseudohyperbolic space K m is constructed. On the other hand, we show that, in each position of H m , the fixed and moving axodes have the instantaneous screw axis of this position in common. We also give relations between the geodetic curvature and the curvature of the polodes.

One Parameter Elliptic Motions in Three-Dimensional Space

“…Furthermore, some authors have examined studies with respect to one-parameter motions in different spaces e.g. [6,7,9,16] Especially an ellipsoid has a great number of applications to various domains of mathematics, physics, geodesy, crystallography. Thus, ellipsoids play an essential role in such areas as probability and statistics [4], fluid dynamics and mechanics [2,8,17], reference ellipsoid [14], thermal ellipsoid [11].…”

On a Spacelike Line Congruence Which Has the Parameter Ruled Surfaces as Principal Ruled Surfaces

“…A large number of papers have been published in the literature which deal with line congruences in both Minkowski space and Euclidean space (See for instance Refs. ( [1][2][3][4]10,[12][13][14][15][16]19,20]). The main interest of this paper is to introduce the E. Study's dual line coordinates in the dual Lorentzian 3-space D 3 1 .…”

A Study On Geometry of Spatial Kinematics in Lorentzian Space

“…Obtained eight homogeneous coordinates divide into two sets of four, each of them represents a vector in a Euclidean 4−space. There are many papers in shed light on this elegant notion [3,5,6,11,12]. Especially, spatial kinematics of points and lines in Euclidean space have been studied by Ravani and Roth [9].…”