Spinor Representations of Involute Evolute Curves in $\mathbb{E}^3$

Reconfiguration of a Rolling Sphere: A Problem in Evolute-Involute Geometry

This paper provides a new perspective to the problem of reconfiguration of a rolling sphere. It is shown that the motion of a rolling sphere can be characterized by evoluteinvolute geometry. This characterization, which is a manifestation of our specific selection of Euler angle coordinates and choice of angular velocities in a rotating coordinate frame, allows us to recast the three-dimensiona...

the involute-evolute offsets of ruled surfaces

in this study, a generalization of the theory of involute-evolute curves is presented for ruledsurfaces based on line geometry. using lines instead of points, two ruled surfaces which are offset in the senseof involute-evolute are defined. moreover, the found results are clarified using computer-aided examples

Invariant spinor representations of finite rotation matrices

Time-like Involutes of a space-like helix in Minkowski space-time

In this work, we deal with a classical differential geometry topic in Minkowski space-time. First, we prove that there are no timelike involutes of a time-like evolute. In the light of this result, we observed that involute curve transforms to a time-like curve when evolute is a space-like helix with a time-like principal normal. Then, we investigated relationships among Frenet-Serret apparatus...

Scalarproducts of Spinor Field Functionals and State Representations in Nonlinear Spinor Field Quantum Theory

In preceding papers it was shown that in nonlinear spinor theory cross-sections of elementary particle scattering processes can be calculated only if the state representations and their scalar products are explicitly known. To obtain these quantities, functional quantum theory of the nonlinear spinor field was introducedIn this paper it is demonstrated that the introduction of functional scalar...