论文标题
不可压缩测试机构在Riemannian空间中移动的力学
Mechanics of Incompressible Test Bodies Moving in Riemannian Spaces
论文作者
论文摘要
在本文中，我们讨论了在具有非平整曲率张量的Riemannian空间中移动的不可压缩测试机构的机制。对于汉密尔顿运动方程，已经以参数形式获得了解决方案，并且已经讨论了球体上纯粹的陀螺运动的特殊情况。对于大地驱动的情况，当电势等于零时，在特定选择问题的运动常数的情况下，已经完成并说明了大地测量溶液之间的比较。 可以将获得的结果应用于地球物理问题，例如，以描述一滴脂肪或在海洋表面上的油位运动或在某些“生态灾难”期间产生的油位或一点点的油位（例如，在某些“生态灾难”期间产生）或在生物力学问题中的运动或通常在生物力学问题上的运动，例如，与内部结构相同的对象进行策划（均匀的曲线）（均匀的曲线）（均匀的曲线）（生物膜）。
In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form and the special case of the purely gyroscopic motion on the sphere has been discussed. For the geodetic case when the potential is equal to zero the comparison between the geodetic and geodesic solutions have been done and illustrated in the case of a particular choice of the constants of motion of the problem. The obtained results could be applied, among others, in geophysical problems, e.g., for description of the motion of a drop of fat or a spot of oil on the surface of the ocean (e.g., produced during some "ecological disaster") or the motion of continental plates, or generally in biomechanical problems, e.g., for description of the motion of objects with internal structure on different curved two-dimensional surfaces (e.g., transport of proteins along the curved biological membranes).
