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A New Formulation of Classical Mechanics—Part 2

DOI: 10.4236/jamp.2016.45103, PP. 939-966

Keywords: Classical Mechanics, Pendulum, Kepler’s Problem

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Abstract:

In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal equation. In this occasion, we will introduce a new way to solve the temporal equation by curving the horizontal axis (the time axis). In this way, we will be able to see the period of some periodic systems as the length of a certain curve and this will allow us to approximate the period in a different way. We will also be able to solve some problems like the pendulum one without using elliptic integrals. Finally, we will solve Kepler’s problem using all the formalism.

References

[1]  Petrovich, F. (2016) A New Formulation of Classical Mechanics—Part 1. Journal of Applied Mathematics and Physics, 4, 412-431.
http://dx.doi.org/10.4236/jamp.2016.42048
[2]  Goldstein, H. (1950) Classical Mechanics. Eddison-Wesley, Reading, MA.
[3]  http://www.sc.ehu.es/sbweb/fisica_//oscilaciones/no_lineales/nolineal/nolineal_1.html

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