Nonlinear generalized equations of motion for multi-link inverted pendulum systems

Khaled Gamal Eltohamy, Chen-Yuan Kuo

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


In this paper, the equations of motion for a general multi-link inverted pendulum system are derived. Assumptions previously employed to simplify such formulation are removed. The pendulum system is more general and includes nonlinear friction terms to suit various engineering applications. The generalized equations are first developed in the absolute coordinate system using Lagrange’s technique, then a simple linear transformation is proposed to obtain the set of nonlinear equations in the DevanitHartenberg coordinate system. The equations of motion for double and triple link inverted pendulum systems are given as examples for such dynamics equations.

Original languageEnglish (US)
Pages (from-to)505-513
Number of pages9
JournalInternational Journal of Systems Science
Issue number5
StatePublished - 1999

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications


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