The Parametrically Excited Multi-Pendulum

摘要

The stability and motions of a two-pendulum system and a ten-pendulum system under parametric excitation are calculated. The equations of motion are derived in symbolic form via the multibody modelling language, AutoSim~(TM). FORTRAN code written by AutoSim is then utilised to yield the matrices necessary for stability analysis by Floquet theory. The matrices are transferred to MATLAB for eigenvalue determination. FORTRAN simulations are used to illustrate stable and unstable states of the systems according to the excitation level used. Time histories are plotted using the freely available plotter WinEP. The analyses reinforce and complement the contents of the previous paper of Kane and Levinson [1]. They demonstrate the power and ease of use of state-of-the-art symbolic codes for mechanical systems analysis. They also show how a model builder can combine with other common software modules to yield an effective total system.