论文标题
三体问题，隐藏常数，特洛伊木马和wimp
3-Body Problems, Hidden Constants, Trojans and WIMPs
论文作者
论文摘要
这项工作包括两个新的结果 - 主要是两个新的运动常数，用于线性限制的三体问题（例如，对于特洛伊小行星），以及对拉格兰奇等于限制案例的等级三角形解决方案的重要等化等速膜三角概括，从而导致希尔达斯和特洛伊人以及特洛伊人的隐藏常数。这两个结果都是经典的，但是我们还包括了与与wimp的颗粒相关的渐近学发出的牛顿量子重力的新结果，从而解释了像特洛伊木马这样的系统的起源。后者的结果使用了我们对涉及向量和标量电势的Schrödinger方程的半经典力学的概括，此处首次提出，从而为我们的天文椭圆形国家提供了我们的思想的酸测试，以预测WIMP轨迹的量子曲率和扭转。综合效果是为重力系统中的wimps提供新的天体力学，并为经典问题提供新的结果。正如我们将要解释的那样，我们认为这些结果可能有助于了解螺旋星系如何演变成椭圆形的星系。我们的等速镜三角结果的一个简单经典后果给出了一个开普勒类型的$ 4^{\ textrm {th}} $法律，以解决三体问题。这仅限于附录。
This work includes two new results - principally two new constants of motion for the linearised restricted 3-body problem (e.g. for the Trojan asteroids) and an important isosceles triangle generalisation of Lagrange's equilateral triangle solution of the restricted case leading to hidden constants for Hildans as well as Trojans. Both of these results are classical, but we also have included new results on Newtonian quantum gravity emanating from the asymptotics relevant for WIMPish particles, explaining the origin of systems like that of the Trojans. The latter result uses a generalisation of our semi-classical mechanics for Schrödinger equations involving vector as well as scalar potentials, presented here for the first time, thereby providing an acid test of our ideas in predicting the quantum curvature and torsion of WIMPish trajectories for our astronomical elliptic states. The combined effect is to give a new celestial mechanics for WIMPs in gravitational systems as well as new results for classical problems. As we shall explain, we believe these results could help to see how spiral galaxies evolve into elliptical ones. A simple classical consequence of our isosceles triangle result gives a Keplerian type $4^{\textrm{th}}$ Law for 3-body problems. This is confined to the Appendix.
