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 \(\mathsf{E}_2^4\). 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 \(\mathsf{E}_2^4\) and we compute their energy to see the distinction between energies for the curves of elastic and non-elastic case in Minkowski space \(\mathsf{E}_2^4\).
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Körpinar, T., Demirkol, R.C. A New Approach on the Energy of Elastica and Non-Elastica in Minkowski Space E\(_{2}^{4}\) . Bull Braz Math Soc, New Series 49, 159–177 (2018). https://doi.org/10.1007/s00574-017-0047-7
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DOI: https://doi.org/10.1007/s00574-017-0047-7