In this research, we study bienergy and biangles of moving particles lying on the surface of Lorentzian 3-space by using their energy and angle values. We present the geometrical characterization of bienergy of the particle in Darboux vector fields depending on surface. We also give the relationship between bienergy of the surface curve and bienergy of the elastic surface curve. We conclude the paper by providing bienergy-curve graphics for different cases.

中文翻译：

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位于洛伦兹空间表面的运动粒子的双能和双角的新方法

在这项研究中，我们通过利用能量和角度值研究位于洛伦兹3空间表面上的运动粒子的双能和双角。我们根据表面在Darboux矢量场中提出了粒子双能的几何特征。我们还给出了表面曲线的双能与弹性表面曲线的双能之间的关系。我们通过提供针对不同情况的双能曲线图形来结束本文。