Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Demonstratio Mathematica

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: evolutes

Sortuj według:

Ogranicz wyniki do:

Evolutes and involutes of frontals in the euclidean plane

Fukunaga T., Takahashi M.

Demonstratio Mathematica

2015

Vol. 48, nr 2

147--166

We have already defined the evolutes and the involutes of fronts without inflection points. For regular curves or fronts, we can not define the evolutes at inflection points. On the other hand, the involutes can be defined at inflection points. In this case, the involute is not a front but a frontal at inflection points. We define evolutes of frontals under conditions. The definition is a generalisation of both evolutes of regular curves and of fronts. By using relationship between evolutes and involutes of frontals, we give an existence condition of the evolute with inflection points. We also give properties of evolutes and involutes of frontals.

On the involute and evolute curves of the timelike curve in Minkowski 3-space

Bukcu B., Karacan K.

Demonstratio Mathematica

2007

Vol. 40, nr 3

721-732

In this study, we have generalized the involute and evolute curves of the timelike curve in Minkowski 3-Space. Firstly, we have shown that, the length between the timelike curve alpha and the spacelike curve beta is constant. Furthermore, the Frenet-Serret frame of the involute curve beta has been found as dependent on curvatures of the curve alpha. We have determined the involute curve beta is planar in which conditions. Secondly, we have found transformation matrix between the evolute curve beta and the curve alpha. Finally, we have computed the curvatures of the evolute curve beta.