ON THE INTEGRAL INVARIANTS OF KINEMATICALLY GENERATED RULED SURFACES

Document Type: Regular Paper

Authors

Department of Mathematics, Faculty of Sciences and Arts, Inönü University, 44069 Malatya, Turkey

Abstract

In this paper, the dual area vector of a closed dual spherical curve is kinematically generated
and the dual Steineer vector of a motion are extensively studied by the methods of differential geometry.
Jacobi’s Theorems, known for real curves, are investigated for closed dual curves. The closed trajectory
surfaces generated by an oriented line are fixed in a moving rigid body in IR3 , in which the closed dual
curves from E. Study’s transference principle is studied. The integral invariants of these closed ruled
surfaces are calculated by means of the area vector. Moreover, some theorems, results and examples are
given.

Keywords