On the modified least action principle with dissipation

K. Fitzgerald, M. Massoudi, A. Vaidya

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton's formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include non-conservative forces such as friction by using the approach suggested by Wang and co-workers (Lin and Wang, 2014; Wang, 2015). However, it turns out that this modified action is dependent upon the nature and amount of damping in the system and the optimality argument fails to hold for sufficiently large values of the damping coefficient. In this paper, we specifically investigate the modified action principle for the cases of a linearly and cubically damped, nonlinear pendulum.

Original languageEnglish
Pages (from-to)301-311
Number of pages11
JournalEuropean Journal of Mechanics, B/Fluids
StatePublished - 1 Sep 2021


  • Action
  • Damping
  • Dissipation
  • Nonlinear pendulum


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