Passive decomposition of mechanical systems with coordination requirement

Dongjun Lee, Perry Y. Li

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We show the fundamental passive decomposition property of general mechanical systems on a n-dim. configuration manifold M, i.e., when endowed with a submersion h:M→N , where N is a m-dim. manifold (m≤n), their Lagrangian dynamics with the kinetic energy as the Lagrangian can always be decomposed into: 1) shape system, describing the m-dim. dynamics of h(q) on N ; 2) locked system, representing the (n-m)-dim. dynamics along the level set of h; and 3) energetically-conservative coupling between them. The locked and shape systems also individually inherit the Lagrangian structure and passivity of the original dynamics. We exhibit and analyze geometric and energetic properties of the passive decomposition in a coordinate-free manner. An illustrative example on SO(3) is also provided.

Original languageEnglish (US)
Article number6213082
Pages (from-to)230-235
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - 2013


  • Coordination
  • Lagrangian systems
  • decomposition
  • differential geometry
  • passivity


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