Normal vibrations of a general class of conservative oscillators

This paper considers normal vibrations with curvilinear trajectories in a configuration space of systems which are close to systems permitting rectilinear normal modes of vibration. Analysis of trajectories of normal vibrations in the configuration space is used.

[1]  C. Hsu,et al.  ON A RESTRICTED CLASS OF COUPLED HILL'S EQUATIONS AND SOME APPLICATIONS , 1961 .

[2]  R. Rand,et al.  Normal modes and global dynamics of a two-degree-of-freedom non-linear system—I. Low energies , 1992 .

[3]  Ali H. Nayfeh,et al.  On Nonlinear Modes of Continuous Systems , 1994 .

[4]  Y. Mikhlin.  Matching of local expansions in the theory of non-linear vibrations , 1995 .

[5]  Y. Mikhlin,et al.  Conditions for finiteness of the number of instability zones in the problem of normal vibrations of non-linear systems☆ , 1984 .

[6]  Christophe Pierre,et al.  Normal Modes for Non-Linear Vibratory Systems , 1993 .

[7]  R. Rosenberg,et al.  Nonsimilar Normal Mode Vibrations of Nonlinear Systems Having Two Degrees of Freedom , 1964 .

[8]  Alexander F. Vakakis,et al.  Non-similar normal oscillations in a strongly non-linear discrete system , 1992 .

[9]  Richard H. Rand,et al.  A higher order approximation for non-linear normal modes in two degree of freedom systems , 1971 .

[10]  H. C. Plummer.  The Analytical Foundations of Celestial Mechanics , 1942, Nature.

[11]  Valery N. Pilipchuk,et al.  Normal oscillations of a string with concentrated masses on non-linearly elastic supports , 1985 .

[12]  Y. Mikhlin.  The joining of local expansions in the theory of non-linear oscillations , 1985 .

[13]  G. C. Gardner.  Viscous Flow of a Liquid Over a Rotating Surface With Gas Drag , 1963 .

[14]  H. Poincaré,et al.  Les méthodes nouvelles de la mécanique céleste , 1899 .

[15]  R. M. Rosenberg,et al.  The Normal Modes of Nonlinear n-Degree-of-Freedom Systems , 1962 .

[16]  R. Vito.  An Approximate Method of Treating the Nonlinear Vibrations of Certain Two-Degree-of-Freedom Systems , 1972 .

[17]  R. M. Rosenberg,et al.  On Nonlinear Vibrations of Systems with Many Degrees of Freedom , 1966 .

[18]  Christophe Pierre,et al.  Non-linear normal modes and invariant manifolds , 1991 .

[19]  A. M. Lyapunov.  The general problem of the stability of motion , 1992 .

[20]  L. I. Manevich,et al.  On periodic solutions close to rectilinear normal vibration modes: PMM vol. 36, n≗6, 1972, pp. 1051–1058 , 1972 .

[21]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .