A novel approximation method for the solution of weakly nonlinear coupled systems

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In this paper, we describe and illustrate the application of a novel approximation technique for coupled, nonlinear dynamic systems. The technique begins by obtaining the analytical (or approximate analytical) solutions to the uncoupled system. Then, these solutions are used to approximate particular terms in the fully-coupled, nonlinear system in such a way that the target system is amenable to (approximate) analytical solution algorithms. This work forms part of a larger effort to develop robust control systems for large-scale industrial manipulators. To this end, the final example examined in this work considers the FutureForge manipulator: a state-of-the-art manipulator which forms part of a next-generation forging platform under development at the Advanced Forming Research Centre in Glasgow. To show the breadth of applications of our approach, we also apply it to more widely-recognised models like the Rayleigh and Van der Pol oscillators. In both of these cases, we consider a system of two oscillators each having dynamic behaviour described by Rayleigh/Van der Pol oscillators and coupled together through the resulting damping matrices.
Original languageEnglish
Pages (from-to)16271-16292
Number of pages22
JournalNonlinear Dynamics
Issue number17
Early online date14 Jul 2023
Publication statusPublished - 30 Sept 2023


  • analytical methods
  • coupled systems
  • industrial manipulators
  • linearisation
  • nonlinear oscillators
  • reducing uncertainty


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