本帖最後由 hunray 於 2012-8-3 22:07 編輯
印裔16歲天才 解開牛頓350年難題..sanmartin 發表於 2012-5-27 16:46 
Conducting an internship at the Chair of Fluid Mechanics at TU Dresden, Shouryya Ray encountered two ordinary differential equations which are special cases of Newton's law that the derivative of the momentum of a particle equals the forces acting on it. In the first one, which describes the motion of a particle in a gas or fluid, this force is the sum of a damping force, which depends quadratically on the velocity, and the (constant) gravitational force.
Here, u and v are the horizontal and vertical velocity, respectively.
and describes the trajectory of the center point z(t) of a spherical particle during a normal collision with a plane wall. (...)
Let us come back to problem (1) which was the starting point of the media stories. In the context of Shouryya Ray's work it was an unfortunate circumstance, that a recent article from 2007'8 claims that no analytical solution of problem (1) was known, or that it was known only in special cases, namely falling objects9. This might have misled Shouryya Ray who was not aware of the classical theory of ordinary differential equations. (...)
To conclude, Shouryya Ray has obtained analytic solutions of the problem (1), by transforming it successively to the problems (3)-(5), and by applying a recent result of D. Dominici in order to obtain a recursive formula for the coefficients of the power series representation of ψ. He then validated his results numerically. Given the level of prerequisites that he had, he made great progress. Nevertheless all his steps are basically known to experts and we emphasize that he did not solve an open problem posed by Newton. (...)
We hope that this small text gives the necessary information to the mathematical community, and that it allows the community to both put in context and appreciate the work of Shouryya Ray who plans to start a career in mathematics and physics.
http://francisthemulenews.wordpress.com/2012/05/29/el-problema-de-newton-y-la-solucion-que-ha-obtenido-shouryya-ray-16-anos/ |
