Hyperbolic Pseudoinverses for Kinematics in the Euclidean Group

Hyperbolic pseudoinverses for kinematics in the Euclidean group

The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions SE(3). The associated Jacobian matrices map into its Lie algebra se(3), the space of twists describing infinitesimal motion of a rigid body. Control methods generally require knowledge of an inverse for the Jacobian. However for an arm with fewe...

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...

Euclidean, Spherical and Hyperbolic Trigonometry

This is a collection of some standard formulae from Euclidean, spherical and hyperbolic trigonometry, including some standard models of the hyperbolic plane. Proofs are not given.

Whirl-similitudes, Euclidean Kinematics, and Non-euclidean Geometry

From the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups

‎The Lorentz transformation of order $(m=1,n)$‎, ‎$ninNb$‎, ‎is the well-known ‎Lorentz transformation of special relativity theory‎. ‎It is a transformation of time-space coordinates of the ‎pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and ‎$n$ space dimensions ($n=3$ in physical applications)‎. ‎A Lorentz transformation without rotations is called a {it boost}‎. ‎Commonly‎, ‎the ...