caa a22 4500 445362073 CHVBK 20180317142918.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s11071-010-9921-1 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9921-1 Lagrangian mechanics of overparameterized systems [Elektronische Daten] [John Hurtado, Andrew Sinclair] Common methods to model the motion of mechanical systems include minimal coordinates and redundant coordinates. Classical presentations of Lagrangian mechanics have focused on these coordinate descriptions. However, sometimes an alternative type of description using overparameterized coordinates is more suitable, in order to avoid coordinate singularities or to simplify the equations of motion. Examples in astrodynamics include the Euler parameters for attitude dynamics and the orbital elements of the two-body problem. This paper investigates issues involved with these descriptions. For these system descriptions the mass matrix is singular, and Lagrange's equations do not provide a unique solution for the generalized accelerations. A set of selective constraints are applied to determine a unique solution. One approach for selecting the constraints is to select holonomic constraints. These constraints serve a fundamentally different role from the redundant-coordinate constraints, which are applied while deriving the equations of motion. Along with these constraints, initial-condition constraints on the generalized coordinates and generalized velocities are needed. Springer Science+Business Media B.V., 2011 Lagrangian mechanics nationallicence Generalized coordinates nationallicence Holonomic constraints nationallicence Euler parameters nationallicence Orbital elements nationallicence Hurtado John Department of Aerospace Engineering, Texas A&M University, 77843, College Station, TX, USA aut Sinclair Andrew Department of Aerospace Engineering, Auburn University, 211 Davis Hall, 36849, Auburn, AL, USA aut Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 201-212 0924-090X 66:1-2<201 2011 66 11071 https://doi.org/10.1007/s11071-010-9921-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9921-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hurtado John Department of Aerospace Engineering, Texas A&M University, 77843, College Station, TX, USA aut NATIONALLICENCE 700 1- Sinclair Andrew Department of Aerospace Engineering, Auburn University, 211 Davis Hall, 36849, Auburn, AL, USA aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 201-212 0924-090X 66:1-2<201 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer