Bumbura O. Bifurcations and stability balanced systems consistently connected pendulums under the force

. Dissertation is about the research of the stability of vertical and non-vertical balanced positions of single and double overturned mathematical pendulums under the follower force. Research has shown that with fluent change of angled or linear eccentricity of follower force there are skipped moves from balanced condition to unbalanced. Influence of resilient elements of pendulum is analyzed. It's been shown that pendulum with soft characteristics has maximum devia-tion from the vertical and it keeps its balanced position. In the case of pendulum with rigid characteristics non-vertical position is achieved with less angle of deviation than with elastic element of linear type. In the test with mixed characteristics of elastic elements, there is continuous dependence of angles of deviation of double pendulum from angled eccentricity of follower force. Graphs show that mixed characteristics of double pendulum increase maximum amount of balance to 7. The built phase portraits of single and double pendulums definitely confirm achieved results.