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John Schultz

Newton knew about "Verlet": described in Principia

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While Verlet integration* is relatively new in the game industry, the concept has been around a very long time: From http://citeseer.ist.psu.edu/hairer03geometric.html: See section 1.3, page 4. Loup Verlet found "his" method described in Newton's Principia (with diagram), which was used to prove Kepler's second law (1687). Richard Feynman also quoted the concept and diagram from Principia. C. Störmer (1907) also described the method as did J.F. Encke (1860) and more. It turns out that "Verlet" has been rediscovered many times. Thus, the method is referred to as the "Newton-Störmer-Verlet-Leapfrog method". Excellent graphs and diagrams, with a comparison to a Runge method are also shown. An interesting paper for those interested in integrators and their history. The authors of this paper wrote Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations. *Many developers have been using "Semi-implicit" Euler for years before Verlet became popular: the two methods are equivalent.

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Newton also said that only twelve spheres can touch a central identical sphere while some other guy said 13. It took 50 years before it was proved that Newton was correct.

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Also impressive is that Newton wrote Principia in only 18 months, and that the work is "The Mathematical Principles of Natural Philosophy".

Not bad for an inattentive student whose mother wanted him to be a farmer! That is, if you are a student and not doing well (and perhaps your mother wants you to be a farmer ;-) ), you may go on to do great things (don't give up due to poor initial performance or weak teachers).

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Quote:
Original post by John Schultz
Also impressive is that Newton wrote Principia in only 18 months, and that the work is "The Mathematical Principles of Natural Philosophy".

Not bad for an inattentive student whose mother wanted him to be a farmer! That is, if you are a student and not doing well (and perhaps your mother wants you to be a farmer ;-) ), you may go on to do great things (don't give up due to poor initial performance or weak teachers).


This seems to be a common recurring characteristic of history's great geniuses. Interestingly it seems mostly all have been, for the most part, self-educated (in other words, their principal education came external to any formal educational institutions, i.e. some still had tutors on the side, etc.).

A quote I've always enjoyed from Mark Twain:

"I have never let my schooling interfere with my education."

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Guest Anonymous Poster
Wow Jon Shultz, very impressive. It looks like this Verlet did not read his history book and was too quickly to declare a new re-invention of a 300 year old method. You know in the old time, all of these explicitly integration methods where known as direct consequences of finite differences formulation, but no one was claiming a new break trough for each permutation of the differences.

You know what would be even more impressive, jon Shulz? if you keep reading maybe you will find that there is not such thing as semi implicit integration, if there was then how can it be applied to a first order differential equation, or this method of yours is only useful for integration of acceleration and velocities.

Hey just Shultz, fallowing the half empty half full logic, since the semi implicit integration is haft way between implicit and explicit, could some one say that your semi implicit method, can be call semi explicit. How about 0.5 * (implicit + explicit)

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Yep, any such relatively trivial thing is discovered and discovered over and over.

(sidenote: if this AP is same AP i'm thinking about, and same AP who derailed some other thread recently, just ban & end of story.)

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