caa a22 4500 475797345 CHVBK 20180406123728.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/PL00001521 doi (NATIONALLICENCE)springer-10.1007/PL00001521 Lie theory, Riemannian geometry, and the dynamics of coupled rigid bodies [Elektronische Daten] [F. C. Park, M. W. Kim] Abstract.: In this article we formulate, in a Lie group setting, the equations of motion for a system of n coupled rigid bodies subject to holonomic constraints. A mapping $f: { \cal {M} \rightarrow \cal {N}$ is constructed, where $\cal M$ is the m-dimensional configuration manifold of the system, and $\cal{N} = \rm{SE(3)} \times \cdots \times \rm{SE(3)}$ (n copies) is endowed with the left-invariant Riemannian metric h corresponding to the total kinetic energy of the system, where SE(3) is the special Euclidean group. The generalized inertia tensor of the system is given by the pullback metric $f^*h$ ; the equations of motion are then the geodesic equations on $\cal M$ with respect to this metric. We show how this coordinate-free formulation leads directly to a factorization of the generalized inertia tensor of the form ${\cal S}^T {\cal L}^T {\cal H} {\cal L} {\cal S}$ , where $\cal S$ is a constant block-diagonal matrix consisting only of kinematic parameters, $\Cal H$ is a constant block-diagonal matrix consisting only of inertial parameters, and ${\cal L}$ is a block lower-triangular matrix composed of Adjoint operators on se(3). Such a factorization is useful for various multibody system dynamics applications, e.g., inertial parameter identification, adaptive control, and design optimization. We also show how in many practical situations ${\cal N}$ can be reduced to a submanifold, thereby considerably simplifying the derivation of the equations of motion. Our geometric formulation not only suggests ways to choose the best coordinates for analysis and computation, but also provides high-level insight into the structure of the equations of motion. Birkhäuser Verlag, Basel,, 2000 Key words. Dynamics, rigid body, Euclidean group, multibody system nationallicence Park F. C. School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea, e-mail: fcp@plaza.snu.ac.kr, KR aut Kim M. W. School of Electrical Engineering, Korea University, Seoul 136-701, Korea, e-mail: mwkim@kuccnx.korea.at.kr, KR aut https://doi.org/10.1007/PL00001521 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00001521 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Park F. C. School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea, e-mail: fcp@plaza.snu.ac.kr, KR aut NATIONALLICENCE 700 1- Kim M. W. School of Electrical Engineering, Korea University, Seoul 136-701, Korea, e-mail: mwkim@kuccnx.korea.at.kr, KR aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer