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2 International Letters of Chemistry, Physics and Astronomy

2 2013

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Novel Theory of Mathematical Pendulum. Part 2

Pluta Z., Hryniewicz T.

International Letters of Chemistry, Physics and Astronomy

2013

Vol. 9, iss. 2

186-201

The paper is concerned on a new adequate theory of a simple mathematical pendulum. Part 1 of the paper was devoted to the behaviour of pendulum in particular points, that is central and terminal/extremum ones. This Part 2 of the theory begins with the analysis of path length of the pendulum weight. Then the kinetics of the pendulum weight is analyzed by separating and the descriptions of differentiated motion of this body in the consecutive neighbouring space-times corresponding with particular quarter-periods. It is about accelerated free variable motion and the following after it a retarded motion of this kind, and then again accelerated, etc. In the summary, further elaborations in the subject are forecasted, regarding both dynamics and energy of the flat mathematical pendulum. It is indicated that the necessity to “rethink” many existent theories is of importance.

Novel Theory of Mathematical Pendulum. Part 1

Pluta Z., Hryniewicz T.

International Letters of Chemistry, Physics and Astronomy

2013

Vol. 9, iss. 2

136-145

In the paper, a new adequate theory of a simple mathematical pendulum is presented. This paper consists of two parts. In Part 1, the behaviour of pendulum in particular points, that is in central and terminal/extremum ones have been analyzed very carefully in detail. System of forces in these points was considered with a special attention turned towards the terminal points where the equilibrium of forces occurs and in the next moment the lack of that equilibrium takes place with the proof of the open polygon of forces as the condition of beginning of accelerated free variable motion. Part 2 of the paper is to be devoted to the kinetics of the pendulum weight presented by separating in it the descriptions of differentiated motion of this body in the consecutive neighbouring space-times corresponding with particular quarter-periods. In the conclusion, further elaborations in the subject are forecasted, regarding both dynamics and energy of the flat mathematical pendulum.