Jalnapurkar, S. M.; Marsden, J. E. Stabilization of relative equilibria. II. (English) Zbl 1056.70514 Regul. Chaotic Dyn. 3, No. 3, 161-179 (1998). Summary: We obtain feedback laws to asymptotically stabilize relative equilibria of mechanical systems with symmetry. We use a notion of stability ‘modulo the group action’ developed by G. W. Patrick [J. Geom. Phys. 9, No. 2, 111–119 (1992; Zbl 0761.58017)]. We deal with both internal instability and instability of the rigid motion. The methodology is that of potential shaping, but the system is allowed to be internally underactuated, i.e., have fewer internal actuators than the dimension of the shape space.Part I, IEEE Trans. Autom. Control 45, No. 8, 1483–1491 (2000; Zbl 0985.70015)}. Cited in 5 Documents MSC: 70Q05 Control of mechanical systems 70K20 Stability for nonlinear problems in mechanics 93D15 Stabilization of systems by feedback Citations:Zbl 0985.70015; Zbl 0761.58017 PDFBibTeX XMLCite \textit{S. M. Jalnapurkar} and \textit{J. E. Marsden}, Regul. Chaotic Dyn. 3, No. 3, 161--179 (1998; Zbl 1056.70514) Full Text: DOI