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Why is the angular momenta is solved in the B-frame while other GEBT governing equation set are written in the a-frame?

  1. Byeonguk Im

    In the reference article by Yu and Blair, "GEBT A general-purpose ... ", the variational formulation for angular momenta and its corresponding discretized equation are expressed in the B-frame. 

     

    Is it because the angular momenta equation will further include some cross-products if it is converted to the a-frame?

     

    Could anybody help me with some explanations? 

     

    Regards

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    Replying to Byeonguk Im

    1. Wenbin Yu

      You are right that angular momenta are not scalars, expressing in a different coordinate system will require coordinate transformation, while such quantities are usually given in b frame, used for performing cross-sectional analysis using VABS. ---- Emailed forum response from wenbinyu@purdue.edu

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    2. Dewey H Hodges

      Just as in Euler’s dynamical equations, where the rigid-body inertia properties and the angular velocity vector are expressed in the basis of the moving body, so also are these angular momenta. This is the simplest way to write Euler’s dynamical equations. It’s not true that all quantities are in the b frame. Actually, K, F, M, P, H are all in B along virtual rotation and virtual displacement. Actually, displacement, rotation, generalized strains gamma and kappa are all in b. Please consult Nonlinear Composite Beam Theory by Hodges (AIAA, 2006) chapter 5. The reasoning should be clearer. ---- Emailed forum response from dhodges@gatech.edu

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    3. Byeonguk Im

      Thanks a lot Prof. Yu and Prof. Hodges for your responses. I understood it well. 

      Regards,

      Byeonguk

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