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Bondarenko, L. A.; Kirpichnikova, E. S.; Kirpichnikov, S. N.

The stability of linear periodic Hamiltonian systems under non-Hamiltonian perturbations. (English. Russian original) Zbl 0884.58056

J. Appl. Math. Mech. 59, No. 6, 829-836 (1995); translation from Prikl. Mat. Mekh. 59, No. 6, 867-876 (1995).
Summary: A definition of strong stability and strong instability is proposed for a linear periodic Hamiltonian system of differential equations under a given non-Hamiltonian perturbation. Such a system is subject to the action of periodic perturbations: an arbitrary Hamiltonian perturbation and a given non-Hamiltonian one. Sufficient conditions for strong stability and strong instability are established. Using the linear periodic Lagrange equations of the second kind, the effect of gyroscopic forces and specified dissipative and non-conservative perturbing forces on strong stability and strong instability is investigated on the assumption that the critical relations of combined resonances are satisfied.

MSC:

37C75 Stability theory for smooth dynamical systems

Keywords:

strong stability; strong instability; linear periodic Hamiltonian system; non-Hamiltonian perturbation
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References:

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