On Sufficient Conditions of Stability of the Permanent Rotations of a Heavy Triaxial Gyrostat

Springer Science and Business Media LLC - Tập 14 - Trang 265-280 - 2014
M. Teresa de Bustos Muñoz1, Juan Luis García Guirao2, Juan Antonio Vera López3, Antonio Vigueras Campuzano2
1Departmento de Matemática Aplicada, Universidad de Salamanca, Salamanca, Spain
2Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, Cartagena, Spain
3Centro Universitario de la Defensa. Academia General del Aire. Universidad Politécnica de Cartagena, Santiago de la Ribera, Spain

Tóm tắt

In this work using as a main tool geometric–mechanics methods we study the permanent rotations of a particular type of heavy triaxial gyrostat. Also, we obtain sufficient conditions of stability of the permanent rotations found previously through the Energy–Casimir method.

Tài liệu tham khảo

Anchev, A.: On the stability of permanent rotations of a heavy gyrostat. J. Appl. Math. Mech. 26(1), 26–34 (1962) Anchev, A.: Permanent rotations of a heavy gyrostat having a stationary point. J. Appl. Math. Mech. 31(1), 48–58 (1967) Cavas, J.A., Vigueras, A.: An integrable case of a rotational motion analogous to that of Lagrange and Poisson for a gyrostat in a Newtonian force field. Celest. Mech. Dyn. Astron. 60, 317–330 (1994) Cochran, J.E., Shu, P.H., Rews, S.D.: Attitude motion of asymmetric dual-spin spacecraft. J. Guid. Control Dyn. 5, 37–42 (1982) Drofa, V.N.: On the permanent axes of motion for a heavy gyrostat near an immovable point. J. Appl. Math. Mech. 25(5), 1411–1419 (1961) Elipe, A., Lanchares, V.: Two equivalent problems: gyrostats in free motion and parametric Hamiltonians. Mech. Res. Comm. 24, 583–590 (1997) Guirao, J.L.G., Vera, J.A.: Dynamics of a gyrostat on cylindrical and inclined Eulerian equilibria in the three body problem. Acta Astronautica 66, 595–604 (2010) Guirao, J.L.G., Vera, J.A.: Lagrangian relative equilibria for a gyrostat in the three body problem. J. Phys. A Math. Theor. 43(19), 1–16 (2010) Kalvouridis, T.J., Tsogas, V.: Rigid body dynamics in the restricted ring problem of \(n+1\) bodies. Astrophys. Space Sci. 282(4), 751–765 (2002) Kalvouridis, T.J.: Stationary solutions of a small gyrostat in the Newtonian field of two bodies with equal masses. Nonlinear Dyn. 61(3), 373–381 (2010) Leimanis, E.: The general problem of the motion of coupled rigid bodies about a fixed point. Springer, Berlin (1965) Marsden, A., Ratiu, T., Weinstein, A.: Semidirect products and reduction in mechanics. Trans. Am. Math. Soc. 281, 147–177 (1984) Ortega, J.P., Ratiu, T.S.: Stability of hamiltonian relative equilibria. Nonlinearity 12(3), 693–720 (1999) Osepashvili, V.Z., Sulikashvili, R.S.: On the stability and bifurcation of the steady state motions of a heavy gyrostat. J. Appl. Math. Mech. 45(3), 19–421 (1981) Rumiantsev, V.V.: On the stability of motion of gyrostats. J. Appl. Math. Mech. 25, 9–19 (1961) Rumiantsev, V.V.: On the stability of motion of certain types of gyrostats. J. Appl. Math. Mech. 25, 1158–1169 (1961) Staude, O.: Permanente Drehungen. Crelles J. Reine Angew. Math. 113, 318 (1894) Tsodokova, N.S.: On the permanent axes of rotation of a gyrostat with a fixed point. J. Appl. Math. Mech. 29(6), 1296–1300 (1965) Tsogas, V., Kalvouridis, T.J., Mavraganis, A.G.: Equilibrium states of a gyrostat satellite moving in the gravitational field of an annular configuration of \(n\) big bodies. Acta Mechanica 175(1–4), 181–195 (2005) Vera, J.A., Vigueras, A.: Hamiltonian dynamics of a gyrostat in the n-body problem: relative equilibria. Celest. Mech. Dyn. Astron. 94(3), 289–315 (2006) Vera, J.A.: Eulerian equilibria of a triaxial gyrostat in the three body problem: rotational Poisson dynamics in Eulerian equilibria. Nonlinear Dyn. 55(1–2), 191–201 (2009) Volterra, V.: Sur la théorie des variations des latitudes. Acta Mathematica 22, 201–357 (1899)