Oscillations of mechanical systems that do not become linear when the parameter vanishes : PMM vol. 42, no. 6, 1978, pp. 1039–1048

The results of investigations in 1] are extended to multidimensional systems that become nonlinear at μ = 0. Two-dimensional mechanical systems were investigated in 2,3]. The characteristic equations of systems considered here contain in the critical system either a pair of pure imaginary roots or two zero roots with one or two groups of solutions and n roots with negative real parts in the adjoint system. It is shown that the investigation of such systems necessitates the imposition on the system of some constraints that supplement those specified in 1], The auxilliary function u⁽¹⁾_k (θ) used in the determination of Liapunov's function is derived by a different method than in 1 – 3], In two of the three investigated cases the problem is reduced to the determination of roots of some integral real irrational function. An example is presented.