A New Approach on the Energy of Elastica and Non-Elastica in Minkowski Space E 24

Abstract

In this work, we firstly describe conditions for being elastica for a moving particle corresponding to different type of space curves in Minkowski space E24. Then, we investigate the energy on the elastic curves corresponding to a particular particle in the space and we also exploit its relationship with energy on the same particle in the Frenet vector fields. Finally, we characterize non-elastic curves in E24 and we compute their energy to see the distinction between energies for the curves of elastic and non-elastic case in Minkowski space E24. © 2017, Sociedade Brasileira de Matemática.