The method of Lyapunov functions in problems of multistability of motion
type: Item
instance of: scholarly article
title: The method of Lyapunov functions in problems of multistability of motion
zbMATH Open document ID: 0677.70023
DOI: 10.1016/0021-8928(87)90001-3
author: A. B. Aminov
author: T. K. Sirazetdinov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1987-01-01T00:00:00Z
review text: The multistability of motion is defined as the property whereby different groups of variables describing the motion have different types of stability, e.g., one group has stability in the small, another has asymptotic stability, and another has boundedness etc. The method of Lyapunov functions is used to prove theorems on multistability which are then used to study the stability of motion of winged aircraft with respect to groups of variables. In existing definitions and studies of stability it is usually assumed that the phase coordinates have the same type of stability, e.g., asymptotic or uniform, etc. In practice, however, say when synthesizing aircraft trajectories, we need to take account of different requirements imposed on the behaviour of different groups of phase coordinates. For instance, when considering the space manoeuvres of an aircraft with constant load factor, it is important to obtain asymptotic stability with respect to the angles of attack and sideslip, while only uniform stability with respect to the angles of pitch, yaw, and rotation is needed. The angles of pitch, yaw, and rotation can themselves have any values, i.e., their stable behaviour is not required. In short, the individual coordinates or groups of coordinates of the same system can have different types of stability, say asymptotic or uniform. We then speak of the multistable motion of the system.
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4110209
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: multistability of motion
zbMATH Keywords: space manoeuvres of an aircraft
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
full work available at URL: 0021-8928(87)90001-3
OpenAlex ID: W2011030667
cites work: Q5801898
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description: scientific article; zbMATH DE number 4110209