Separation of the equations of motion in two-dimentional gravitatrional pendulums
Articles
Olga Lavcel-Budko
Vilniaus Gedimino technikos universitetas
Aleksandras Krylovas
Vilniaus Gedimino technikos universitetas
Paulius Miškinis
Vilniaus Gedimino technikos universitetas
Published 2012-12-25
https://doi.org/10.15388/LMR.B.2012.06
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Keywords

pendulum
asymptotic methods
nonlinear waves
nonlinear wavering

How to Cite

Lavcel-Budko O., Krylovas A. and Miškinis P. (2012) “Separation of the equations of motion in two-dimentional gravitatrional pendulums”, Lietuvos matematikos rinkinys, 53(B), pp. 31–36. doi: 10.15388/LMR.B.2012.06.

Abstract

We solve the classical problem-model of the oscillation of the gravitational pendulum on the elastic thread. This task was formulated, but it is not completely solved in the classical K. Magnus
monograph “Wavering”. With additional assumptions about the analyzed model in question (mass
conservation law and considerations about certain physic) system of the differential equations of the
two second-order nonlinear oscillation transformed into a third order nonlinear differential equation
which is solved numerical approximate using the Maple program. The solution is compared with
asymptotic in a long time range.

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