Separation of the equations of motion in two-dimentional gravitatrional pendulums - Lavcel-Budko, Olga; Krylovas, Aleksandras; Miškinis, Paulius (Lietuvos matematikos rinkinys, 2012)
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. Magnusmonograph “Wavering”. With additional assumptions about the analyzed model in question (massconservation law and considerations about certain physic) system of the differential equations of thetwo second-order nonlinear oscillation transformed into a third order nonlinear differential equationwhich is solved numerical approximate using the Maple program. The solution is compared withasymptotic in a long time range.
Keywords: pendulum; asymptotic methods; nonlinear waves; nonlinear wavering