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

Shamolin, M. V.

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)

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