vendredi 1 juin 2012

Shouryya Ray Solution To 350-Year-Old Issac Newton Puzzle On Search By Physicists

Shouryya Ray caught the attention of physicists and mathematicians all over the world when it was reported that he finally cracked and solved the 350-year-old Isaac Newton puzzle.

Shouryya Ray is a 16-year-old Indian-born student who moved to Germany four years ago to continue his studies. Recently, he won second prize in the math and informatics category for Germany’s Jugend Forscht student science competition where he discussed puzzles for physics students.

In his paper entitled “Analytical Solution of Two Fundamental Unsolved Problems of Particle Dynamics”, he tackled two fundamental particle dynamics theories that physicists have previously only been able to approximate by using computers with partial solutions: How do you account for air resistance in calculating the trajectory of ball thrown out at an angle? And precisely how does a ball thrown against the wall rebound?

The teen’s solutions allow exact calculations of a trajectory under gravity and subject to air resistance. In other words, an item’s flight path can be calculated and predictions can be made of how the object will hit and bounce off a barrier. The two questions were first posed in the 17th and 19th centuries.

Shourryya Ray Cracked Isaac Newton Puzzle

Since Ray’s paper was just a school project submitted for a contest without the necessary peer review, experts are reluctant to weigh in. Richard Fitzpatrick, a physicist at the University of Texas told MSN:

“This story seems rather suspicious.None of the news reports give any details of the calculation. None of the people who hailed Shouryya Ray as a genius are scientists, and none of them give the impression that they have seen the calculation in question. It is impossible to gauge the scientific merit of the calculation until it is made public.”

With this news the subject of various forums, Ayre posted at on what seems the specific details of the first problem which Ray solved in his paper.

Find the motion of a point particle traveling in uniform gravity, with drag proportional to the square of its speed. The governing equations are:

Isaac Newton Equation

where u and v are the horizontal and vertical components of the velocity of the particle, g is the gravitational acceleration, and alpha is a coefficient of drag, so that the deceleration due to drag is alpha*(u²+v²). The initial conditions are that v(0) = v_0 > 0, and u(0) = u_0 > 0.

By viewing an enhanced image of his picture above holding his solution, Ayre added that Ray’s solution might be:

Shourrya Ray's Solution to Isaac Newton Puzzle

where he claims Ray has found the velocity in terms of Taylor series in time.

Another interesting finding was posted by Klackity from Reedit where the problem lies on a ‘particle that takes a path in the space of velocities. Such a path uniquely determines a path in the space of positions, given starting position.’

He then verified Shouryya Ray’s claims that the following function below represented by, f, is constant on the path the particle makes in the space of velocities using Maple software, a commercial computer algebra system.

Function f

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