The Poincaré equations, also known as Lagrange’s equations in quasicoordinates, are revisited with special attention focused on a diagonal form. The diagonal form stems from a special choice of generalized speeds that were first introduced by Hamel (Hamel, G., 1967, Theorctische Mechanik, Springer-Verlag, Berlin, Secs. 235 and 236) nearly a century ago. The form has been largely ignored because the generalized speeds create so-called Hamel coefficients that appear in the governing equations and are based on the partial derivative of a mass-matrix factorization. Consequently, closed-form expressions for the Hamel coefficients can be difficult to obtain. In this paper, a newly developed operator overloading technique is used within a simulation code to automatically generate the Hamel coefficients through an exact partial differentiation together with a numerical evaluation. This allows the diagonal form of Poincaré’s equations to be numerically integrated for system simulation. The diagonal form and the techniques used to generate the Hamel coefficients are applicable to general systems, including systems with closed kinematic chains. Because of Hamel’s original influence, these special Poincaré equations are called the Hamel representations and their usefulness in dynamic simulation and control is investigated.
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October 2007
Research Papers
The Hamel Representation: A Diagonalized Poincaré Form
Michael C. Sovinsky,
Michael C. Sovinsky
Department of Aerospace Engineering,
Texas A&M University
, 3141 TAMU, College Station, TX 77843-3141
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John E. Hurtado,
John E. Hurtado
Department of Aerospace Engineering,
Texas A&M University
, 3141 TAMU, College Station, TX 77843-3141
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D. Todd Griffith,
D. Todd Griffith
Structural Dynamics Research Department,
Sandia National Laboratories
, P.O. Box 5800, Albuquerque, NM 87185
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James D. Turner
James D. Turner
Dynacs Military and Defense
, Houston, TX 77058
Search for other works by this author on:
Michael C. Sovinsky
Department of Aerospace Engineering,
Texas A&M University
, 3141 TAMU, College Station, TX 77843-3141
John E. Hurtado
Department of Aerospace Engineering,
Texas A&M University
, 3141 TAMU, College Station, TX 77843-3141
D. Todd Griffith
Structural Dynamics Research Department,
Sandia National Laboratories
, P.O. Box 5800, Albuquerque, NM 87185
James D. Turner
Dynacs Military and Defense
, Houston, TX 77058J. Comput. Nonlinear Dynam. Oct 2007, 2(4): 316-323 (8 pages)
Published Online: April 16, 2007
Article history
Received:
December 8, 2005
Revised:
April 16, 2007
Citation
Sovinsky, M. C., Hurtado, J. E., Griffith, D. T., and Turner, J. D. (April 16, 2007). "The Hamel Representation: A Diagonalized Poincaré Form." ASME. J. Comput. Nonlinear Dynam. October 2007; 2(4): 316–323. https://doi.org/10.1115/1.2756062
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