Equilibria, stability and Hamiltonian Hopf bifurcation of a gyrostat in an incompressible ideal fluid

Periodic solutions induced by an upright position of small oscillations of a sleeping symmetrical gyrostat

“…These rotors may rotate with respect to the platform in such a way that the mass distribution within the system as a whole is not altered; this will produce an internal angular momentum, designated as gyrostat momentum, which will be normally regarded as a constant. Note that when this constant vector is zero, the motion of the system is reduced to the motion of a rigid solid, see for instance Figure 1 where a gyrostat in the frame of the three body problem is presented, and [3,4] or [5] for more details on this class of mechanical systems. The objective of this paper is to provide, using the averaging theory, a system of nonlinear equations whose simple zeros provide periodic solutions of the differential system (1).…”

The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field

“…is method was employed in several works such as [15][16][17][18][19][20][21][22][23]. e energy-Casimir method is briefly presented in the following.…”

“…e second category regards the problem of study periodic solutions, bifurcation, and chaos in some problems of rigid body-gyrostat (see, e.g., [11][12][13][14]). e third one is the stability problem of the equilibria in the dynamics of a rigid body-gyrostat moving in an orbit or about its fixed point (see, e.g., [15][16][17][18][19][20][21][22][23]). e current work is interested in studying the stability of permanent rotations for the motion of a charged gyrostat moving due to the combined influence of the magnetic field and Newtonian force field.…”

Control of the motion of an unbalanced heavy ellipsoid in an ideal fluid using rotors

“…Задача об управлении движением шара с помощью двух роторов рассматривалась в работе [12]. Применение роторов для курсовой стабилиза-ции при движении в жидкости изучалось в [15,16,34], а при движении спутника -в [17].…”