The post-Newtonian scheme in multiple systems with post-Newtonian parameters presented by Klioner and Soffel is extended to the post-post-Newtonian （PPN） order for light propagation problem in the solar system. Unde...The post-Newtonian scheme in multiple systems with post-Newtonian parameters presented by Klioner and Soffel is extended to the post-post-Newtonian （PPN） order for light propagation problem in the solar system. Under considering the solar system experiment requirement, a new parameter ε is introduced. This extension does not change the virtue of the scheme on the linear partial differential equations of the potential and vector potential mentioned in previous work. Furthermore, this extension is based on the former work done by Richter and Matzner in one global system theory. As an application, we also consider the deflection of light ray in the global coordinates. And the deflection angle of light ray is obtained with post-Newtonian parameters.展开更多
While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors....While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors.These caustic surfaces,described in a closed form,are also developable surfaces of the same type as the original mirror surface.We provide efficient,algorithmic computation to find the caustic surface of each of the three types of developable surfaces(cone,cylinder,and tangent surface of a spatial curve).We also provide a potential application of the results in contemporary free-form architecture design.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10674099)the National Science Foundation for Young Scientists of China (Grant No. 10925313)the Shandong Provincial Natural Science Foundation,China (GrantNo. ZR2010AQ023)
文摘The post-Newtonian scheme in multiple systems with post-Newtonian parameters presented by Klioner and Soffel is extended to the post-post-Newtonian （PPN） order for light propagation problem in the solar system. Under considering the solar system experiment requirement, a new parameter ε is introduced. This extension does not change the virtue of the scheme on the linear partial differential equations of the potential and vector potential mentioned in previous work. Furthermore, this extension is based on the former work done by Richter and Matzner in one global system theory. As an application, we also consider the deflection of light ray in the global coordinates. And the deflection angle of light ray is obtained with post-Newtonian parameters.
基金Project supported by the European Union and the European Social Fund(No.EFOP-3.6.3-VEKOP-16-2017-00002).Open Access funding provided by European Union and the European Social Fund。
文摘While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors.These caustic surfaces,described in a closed form,are also developable surfaces of the same type as the original mirror surface.We provide efficient,algorithmic computation to find the caustic surface of each of the three types of developable surfaces(cone,cylinder,and tangent surface of a spatial curve).We also provide a potential application of the results in contemporary free-form architecture design.
