![]() ![]() ![]() applied the Poincaré-Birkhoff fixed point theorem and shows that there exist a stable and unstable periodic solution of a forced pendulum of variable length. The Lyapunov exponents and forcing amplitude in controlling the chaotic motion of a driven pendulum is studied in. Work proves the effectiveness of real experimental data of reconfiguration of coupled pendulums on a data flow visual programming using LabVIEW. We begin from some methods of forcing of the analyzed dynamical system. ![]() It can also be treated as a control system due to time-varying control laws of changing its length, as well as it has various applications in mechatronic systems, which include: robots, electro-mechanical systems like induction motors, purely electrical networks like dc-dc power converters, lifting devices like mine elevators or cranes, earthquakes detection based on various concepts of inverted pendulums or even wave energy converters (WEC). The variable-length pendulum may be treated as a second-order nonlinear differential equation with a step function dependent coefficients which can be transformed into equivalent discrete dynamical systems. It can also be applied in simple mechatronic and robotic systems. The new technique can reduce residual vibrations through damping when the desired level of the crane is reached. The results of original numerical simulations show that the extended SAM’s nonlinear dynamics presented in the current work can be thoroughly studied, and more modifications can be achieved. The extended SAM presents a novel SAM concept being derived from a variable-length double pendulum with a suspension between the two pendulums. Finally, an extended model for a variable-length pendulum’s mechanical application being derived from the Swinging Atwood Machine is proposed. At the end of the review, it is concluded that many variable-length pendulums are very demanding in the modeling and analysis of parametric dynamical systems, but basic knowledge about constant-length pendulums can be used as a good starting point in providing much accurate mathematical description of physical processes. Some important physical concepts are verified using dedicated numerical procedures and assessed based on dynamical analysis. Perspectives of future trends are also noted on the basis of various concepts and possible theoretical and engineering applications. An attempt at a unique evaluation of current trends in this field is carried out in accordance with mathematical modeling, dynamical analysis, and original computer simulations. A comprehensive review of variable-length pendulums is presented. ![]()
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