Shamolin, M. V. The definition of relative robustness and a two-parameter family of phase portraits in the dynamics of a rigid body. (English. Russian original) Zbl 0874.70006 Russ. Math. Surv. 51, No. 1, 165-166 (1996); translation from Usp. Mat. Nauk 51, No. 1, 175-176 (1996). The author introduces the notion of relative robustness (structural stability) and illustrates it on an example of a rigid body interacting with a medium. The difference from the classical notion of robustness is that the author considers a \(C^1\)-neighbourhood of a vector field only in a certain class of vector fields, not in the space of all vector fields, and the fields from the neighbourhood should be equivalent to the initial vector field through a homeomorphism close (in \(C^0\)-topology) to the unit homeomorphism. Relative robustness of varying degree is also introduced. Reviewer: Yu.E.Gliklikh (Voronezh) Cited in 5 Documents MSC: 70E15 Free motion of a rigid body 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics 37C75 Stability theory for smooth dynamical systems Keywords:interaction with medium; relative robustness of varying degree; vector field; unit homeomorphism PDF BibTeX XML Cite \textit{M. V. Shamolin}, Russ. Math. Surv. 51, No. 1, 165--166 (1996; Zbl 0874.70006); translation from Usp. Mat. Nauk 51, No. 1, 175--176 (1996) Full Text: DOI