论文标题
在弯曲的空间中游泳的一般理论
General theory of swimming in curved spacetimes
论文作者
论文摘要
在弯曲的空间中游泳是一种现象，弯曲的空间中的自由尸体能够通过执行循环内部运动来推动自己。最初提出建议，进一步提出，在快速内部周期的极限中，净运动将显示一个简单的几何相位特征，其中每个周期的位移不取决于内部运动的时间进程，而仅取决于身体在非热情洋溢的人体中所假定的形状的顺序，例如在非热情的Viscoustic Viscous viscous viscoustic viscous viscous viscous viscous viscous viscous viscous viscous viscous viscous viscous viscous viscous viscous viscous flow reynolds norke norke norks norks norks norks norke norks norks norks norks nork）。在本文中，我们在弯曲的空间中开发了一种一般的，协变量的游泳理论，描述了一种研究一种技术，可以通过将问题映射到特殊相对论中的类似物中，从而研究自由，小型，光线，铰接式物体的运动。我们非常关注快速循环的极限，并研究总体运动可以显示这种几何相相行为的条件。然而，结论是，这种简单的行为仅在非常具体的情况下实现，具体取决于身体的结构，内部运动的特征，初始条件和时空的对称性。而通常，我们的公式可以预测一个更复杂的动力学。
Swimming in curved spacetimes is a phenomenon whereby free bodies in curved spacetimes are able to propel themselves by performing cyclic internal motions. When originally proposed, it was further suggested that, in the limit of fast internal cycles, the net motion would display a simple geometric-phase character, in which the displacement per cycle would not depend on the time progression of the internal motions but only on the sequence of shapes assumed by the body, like a swimmer in a non-turbulent viscous fluid (low Reynolds number). In this paper we develop a general, covariant theory of swimming in curved spacetimes, describing a technique to study the motion of free, small, light, articulated bodies in general relativity by mapping the problem to an analogue in special relativity. We give considerable attention to the limit of fast cycles and investigate the conditions in which the overall motion could display such geometric-phase behavior. The conclusion, however, is that this simple behavior is only realized in very specific circumstances, depending on the structure of the body, characteristics of internal motions, initial conditions, and symmetries of the spacetime; whereas, in general, our formulas predict a more complicated dynamics.
