An efficient direct differentiation approach for sensitivity analysis of flexible multibody systems

Kishor D. Bhalerao, Mohammad Poursina, Kurt S. Anderson

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


This paper presents a recursive direct differentiation method for sensitivity analysis of flexible multibody systems. Large rotations and translations in the system are modeled as rigid body degrees of freedom while the deformation field within each body is approximated by superposition of modal shape functions. The equations of motion for the flexible members are differentiated at body level and the sensitivity information is generated via a recursive divide and conquer scheme. The number of differentiations required in this method is minimal. The method works concurrently with the forward dynamics simulation of the system and requires minimum data storage. The use of divide and conquer framework makes the method linear and logarithmic in complexity for serial and parallel implementation, respectively, and ideally suited for general topologies. The method is applied to a flexible two arm robotic manipulator to calculate sensitivity information and the results are compared with the finite difference approach.

Original languageEnglish (US)
Pages (from-to)121-140
Number of pages20
JournalMultibody System Dynamics
Issue number2
StatePublished - Feb 2010
Externally publishedYes


  • Direct differentiation
  • Divide and conquer scheme
  • Flexible multibody systems
  • Sensitivity analysis

ASJC Scopus subject areas

  • Modeling and Simulation
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications
  • Control and Optimization


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