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Hamel Coefficients for the Rotational Motion of a Rigid Body

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Abstract

A Lagrangian treatment of various forms of the rigid-body equations of motion is presented in this paper, including the most general expressions, which are the Boltzmann-Hamel equations. One key result that enables the derivations is the expression for the Hamel coefficients for the special case of rotational motion of a rigid body. The Hamel coefficients naturally arise in the Lagrange equations for quasi-coordinates. Another key result that enables the derivations is the expression for additional Hamel coefficients that arise when the translational-velocity vector of the mass center is coordinatized (expressed) along body-fixed axes. One interesting discovery is that the Boltzmann-Hamel equations are often misrepresented in standard textbooks. The misrepresentation stems from the fact that care is not exercised to distinguish the functional forms of the kinetic-energy expression.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station, TX, 77843-3141, USA

    J. E. Hurtado (Assistant Professor)

Authors
  1. J. E. Hurtado
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Correspondence to J. E. Hurtado.

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Dedicated to John L. Junkins on the occasion of his sixtieth birthday.

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Hurtado, J.E. Hamel Coefficients for the Rotational Motion of a Rigid Body. J of Astronaut Sci 52, 129–147 (2004). https://doi.org/10.1007/BF03546425

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  • DOI: https://doi.org/10.1007/BF03546425

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