Weyl–Euler–Lagrange equations on twistor space for tangent structure

Twistor spaces are certain complex three-manifolds, which are associated with special conformal Riemannian geometries on four-manifolds. Also, classical mechanic is one of the major subfields for mechanics of dynamical system. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space for classical mechanic. Euler–Lagrange equations are an efficient use of classical mechanics to solve problems using mathematical modeling. On the other hand, Weyl submitted a metric with a conformal transformation for unified theory of classical mechanic. This paper aims to introduce Euler–Lagrage partial differential equations (mathematical modeling, the equations of motion according to the time) for the movement of objects on twistor space and also to offer a general solution of differential equation system using the Maple software. Additionally, the implicit solution of the equation will be obtained as a result of a special selection of graphics to be drawn.

A Novel Approach for the CAM-Follower Mechanism of High Frequency Cutting File Machine

In this work, the re-design of the camfollower mechanism of an industrial cutting file machine is presented. The actual mechanical system includes a forceclosure cam mechanism, which requires an external force to keep the contact between the cam and the follower provided by a spring. This system is substituted by a new cam mechanism of the type of formclosure, which does not require external force. The formclosure camfollower mechanism, also called positive-return cam mechanism, guarantees that the cam surface is always in contact with the follower surface, and is characterized by having constantbreadth. Classical Mechanic Theory performs the study of the kinematic and dynamic characteristics of the cam mechanism analyzed throughout this work. Furthermore, a commercial package software was used to create a virtual model and analyze the motion characteristics of the new cam mechanism.