Abstract
Mechanical systems under the action of positional forces or a combination of positional forces and forces of the type of fourth-order forms with respect to the velocities (non-holonomic Chaplygin systems) as well as non-holonomic systems where there are no dissipative forces, belong to systems with a linear automorphism of a special type. In the case of such systems, stability of the equilibrium positions is only possible in the critical case of some zero and purely imaginary roots; asymptotic stability is impossible when there are zero roots. In the non-resonant case there is formal stability and a family of periodic motions exists similar to a Lyapunov family in the case of Hamiltonian systems and a family of conditionally periodic motions with a set of frequencies which are proportional to the frequencies of a linear system. The problem of the stability in the case of the lower (third and fourth) order resonances is solved. Examples are considered.
Published Version
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