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Far East Journal of Dynamical Systems

Far East Journal of Dynamical Systems
Volume 1, Issue 1, Pages 1 - 24 (December 1999)

A DYNAMICAL SYSTEM THEORETICAL APPROACH TO NEWTONIAN MECHANICS
Shiro Ishikawa (Japan), Takahiro Arai (Japan) and Hiroki Takamura (Japan)

Abstract:
The theory of dynamical systems is generally formulated in the form: “dynamical system theory” = “state equation” + “measurement equation”. Also, it is usually believed that the theory of dynamical systems is modeled on Newtonian mechanics. However, it is not sure. That is because the “measurement equation” is missing in Newtonian mechanics. In order to say that the theory of dynamical systems is modeled on Newtonian mechanics, it suffices to reconstruct “Newtonian mechanics” such as it has the concept of “measurement”. This is our first intention. Through these arguments, the frame of dynamical system theory has become clear. Thus, we can also propose “general system theory”. Since it is expected to be the most general system theory under the spirit of “the mechanical world view”, we believe that it is proper as a standard frame of “system theory”.

Keywords and phrases: measurements, Newtonian equation, dynamical system theory, trajectories, probability.

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P-ISSN: 0972-1118

E-ISSN: 3048-7897

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