Recursive Flexible Multibody System Dynamics Using Spatial Operators.pdfVIP

Journal of Guidance Control and Dynamics vol pp Nov Recursive Flexible Multib o dy System Dynamics using Spatial Op erators A Jain and G Ro driguez y Abstract This pap er uses spatial op erators to develop new spatially recursive dynamics algorithms for exible multib o dy systems The op erator description of the dynamics is identical to that for rigid multib o dy systems Assumedmo de mo dels are used for the deformation of each individual b o dy The algorithms are based on two spatial op erator factorizations of the system mass matrix The rst NewtonEuler factorization of the mass matrix leads to recursive algorithms for the inverse dynamics mass matrix evaluation and comp ositeb o dy forward dynamics for the system The second Innovations factorization of the mass matrix leads to an op erator expression for the mass matrix inverse and to a recursive articulatedb o dy forward dynamics algorithm The primary fo cus is on serial chains but extensions to general top ologies are also describ ed A comparison of computational costs shows that the articulatedb o dy forward dynamics algorithm is much more ecient than the comp ositeb o dy algorithm for most exible multib o dy systems Nomenclature We use co ordinatefree spatial notation Refs in this pap er A spatial velocity of a frame is a dimensional quantity whose upp er elements are the angular velo city and whose lower elements are the linear velo city A spatial for ce is a dimensional quantity whose upp er elements are a moment vector and whose lower elements are a force vector A variety of indices are used to identify dierent spatial quantit