Attitude stability of an orbiting gyrostat in conical equilibrium

Hughes, P. C.

doi:10.2514/3.20024

Cited by 3 publications

(1 citation statement)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The gravity stabilized satellite uses the benefits of gravitational potential energy of the earth rather than the other stabilizers such as different types of thrusters or servo motors, thus it can preserve its batteries energy for other tasks. Gyrostatic effect has been used extensively in gravity stabilized satellites [1][2][3][4][5][6][7][8]. A gyrostat consists of two parts, namely body and rotor (or wheel).…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and Chaos in an Apparent-Type Gyrostat Satellite

Shirazi

Ghaffari-Saadat

2005

Nonlinear Dyn

View full text Add to dashboard Cite

Attitude dynamics of an asymmetrical apparent gyrostat satellite has been considered. Hamiltonian approach and Routhian are used to prove that the dynamics of the system consists of two separate parts, an integrable and a non-integrable. The integrable part shows torque free motion of gyrostat, while the non-integrable part shows the effect of rotation about the earth and asphericity of the satellite's inertia ellipsoid. Using these results, theoretically when the non-integrable part is eliminated, we are able to design a satellite with exactly regular motion. But from the engineering point of view the remaining errors of manufacturing process of the mechanical parts cause that the non-integrable part can not be eliminated, completely. So this case can not be achieved practically. Using Serret-Andoyer canonical variable the Hamiltonian transformed to a more appropriate form. In this new form the effect of the gravity, asphericity, rotational motion and spin of the rotor are explicitly distinguished. The results lead us to another way of control of chaos. To suppress the chaotic zones in the phase space, higher rotational kinetic energy can be used. Increasing the parameter related to the spin of the rotor causes the system's phase space to pass through a heteroclinic bifurcation process and for the sufficiently large magnitude of the parameter the heteroclinic structure can be eliminated. Local bifurcation of the phase space of the integrable part and global heteroclinic bifurcation of whole system's phase space are presented. The results are examined by the second order Poincaré surface of section method as a qualitative, and the Lyapunov characteristic exponents as a quantitative criterion.Nomenclature a 1 , a 2 , a 3 = Directional cosines of the spin axis in the body fixed coordinate. α 1 , α 2 , α 3 , α 4 = Dimensionless parameters of the system. b i j , r i j , j i j = Components of the body, the rotor and the whole satellite moment of inertia tensors respectively, in the body fixed coordinate. β 1 , β 2 , β 3 = Euler angles. φ = Euler angle (rotation angle about xb-axis). G, g b , g r = The satellite, the body and the rotor center of masses, respectively. H = Hamiltonian of the system. h , h 0 , h 1 , h 2 = Normalized Hamiltonian. i 1 , i 2 , i 3 = Unit vectors of the body fixed coordinate. J b , J r , j s = The body, the rotor and the whole satellite moment of inertia tensors respectively, in the body fixed coordinate. J 1 , J 2 , J 3 = Principal moments of inertia of the satellite. K , K 0 K 1 , K 2 = Transformed Hamiltonian. L = Lagrangian of the system. λ i , i = 1, . . . , 6 = Characteristic Lyapunov Exponents. p σ = Generalized momentum associated with σ . θ = Euler angle (rotation about y-axis). R 3 = Moment of inertia of the rotor about the body fixed axis of spin. R = Radius of the satellite's orbit. R = Routhian of the system. 260 K. H. Shirazi and M. H. Ghaffari-Saadat σ,σ = Relative angle and relative angular velocity of the body and the rotor, respectively. T = Kinetic energy.V = Potential ener...

show abstract

Section: Introductionmentioning

confidence: 99%