Relaxed elastic lines of second kind in dual space

Abstract

In this study, we worked on the second kind of relaxed elastic lines on dual spaces which has an important point on kinematic. We also obtained boundary conditions for this type of curves. Moreover, the minimization problem of the energy which occurs with an applied force on an elastic line was discussed. Then, we researched the formed potential energy due to the applied force and derived boundary conditions for that case.

On a variational problem due to the B‐Darboux frame in Euclidean 3‐space

“…Theory of elasticity is a direct part of the differential calculus, [1][2][3][4][5] which is an important topic in analysis, 6,7 physics, chemistry, and engineering. 8 As well as, similar applications of the elasticity theory in different spaces can be found in previous studies.…”