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TSMC was founded in Taiwan in 1987 by Morris Chang as the world's first dedicated semiconductor foundry. It has long been the leading company in its field. [15] [16] When Chang retired in 2018, after 31 years of TSMC leadership, Mark Liu became chairman and C. C. Wei became Chief Executive.
Stranger Things is an American science fiction horror drama television series created by the Duffer Brothers for Netflix.Produced by Monkey Massacre Productions and 21 Laps Entertainment, the first season was released on Netflix on July 15, 2016. The second and third seasons followed in October 2017 and July 2019 respectively, and the fourth season was released in two parts in May and July 2022.
- Mathematical Description
- Solutions
- History
- Other Problems Involving Three Bodies
- N-Body Problem
- External Links
The mathematical statement of the three-body problem can be given in terms of the Newtonian equations of motion for vector positions r i = ( x i , y i , z i ) {\displaystyle \mathbf {r_{i}} =(x_{i},y_{i},z_{i})} of three gravitationally interacting bodies with masses m i {\displaystyle m_{i}} : where H {\displaystyle {\mathcal {H}}} is the Hamilton...
General solution
There is no general closed-form solution to the three-body problem.In other words, it does not have a general solution that can be expressed in terms of a finite number of standard mathematical operations. Moreover, the motion of three bodies is generally non-repeating, except in special cases. However, in 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists an analytic solution to the three-body problem in the form of a Puiseux series, specifically a power series in t...
Special-case solutions
In 1767, Leonhard Euler found three families of periodic solutions in which the three masses are collinear at each instant. See Euler's three-body problem. In 1772, Lagrange found a family of solutions in which the three masses form an equilateral triangle at each instant. Together with Euler's collinear solutions, these solutions form the central configurations for the three-body problem. These solutions are valid for any mass ratios, and the masses move on Keplerian ellipses. These four fam...
Numerical approaches
Using a computer, the problem may be solved to arbitrarily high precision using numerical integration although high precision requires a large amount of CPU time. There have been attempts of creating computer programs that numerically solve the three-body problem (and by extension, the n-body problem) involving both electromagnetic and gravitational interactions, and incorporating modern theories of physics such as special relativity. In addition, using the theory of random walks, an approxim...
The gravitational problem of three bodies in its traditional sense dates in substance from 1687, when Isaac Newton published his Philosophiæ Naturalis Principia Mathematica, when Newton was trying to figure out if any long term stability is possible, especially the system of our Earth, the Moon, and the Sun. He was guided under the major Renaissanc...
The term "three-body problem" is sometimes used in the more general sense to refer to any physical problem involving the interaction of three bodies. A quantum-mechanical analogue of the gravitational three-body problem in classical mechanics is the helium atom,in which a helium nucleus and two electrons interact according to the inverse-square Cou...
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details). Ho...
Chenciner, Alain (2007). "Three body problem". Scholarpedia. 2 (10): 2111. Bibcode:2007SchpJ...2.2111C. doi:10.4249/scholarpedia.2111.The Maldives is the smallest country in Asia. Including the sea, the territory spans roughly 90,000 square kilometres (35,000 sq mi), and a land area of 298 square kilometres (115 sq mi). The Maldives is one of the world's most geographically dispersed sovereign states, and the smallest Muslim-majority country by land area.
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