Optimum energy extraction from rotational motion in a parametrically excited pendulum

Krishnan Nandakumar*, Marian Wiercigroch, Anindya Chatterjee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


A pendulum rotating under vertical base excitation is considered from the viewpoint of energy extraction. Since the uncontrolled system can exhibit complex dynamics, we consider an added control torque and seek the optimal period-1 rotational motion for maximum energy extraction. We find, and confirm through complementary methods, that the limiting optimal motion for harmonic base excitation is piecewise-constant: there are extended dwells at the top and bottom positions with rapid transitions in between. The limiting optimal solution gives about a quarter more energy extraction than uniform rotation, in the limit of no damping. Approximating motions with finite-speed transitions can be almost as good. Base excitations other than pure sinusoids are also considered and the corresponding optima determined.

Original languageEnglish
Pages (from-to)7-14
Number of pages8
JournalMechanics Research Communications
Publication statusPublished - 1 Jul 2012


  • Damping
  • Energy extraction
  • Parametric pendulum
  • Period-1 rotation


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