The Dynamics of Finite-Dimensional Systems Under Nonconservative Position Forces

General theorems on the stability of stationary states of mechanical systems subjected to nonconservative position forces are presented. Specific mechanical problems on gyroscopic systems, a double-link pendulum with a follower force and elastically fixed upper tip, multilink pneumowheel vehicles, a monorail car, and rail-guided vehicles are analyzed. Methods for investigation of divergent bifurcations and catastrophes of stationary states are described

[1]  V. V. Bolotin,et al.  Dynamic Stability of Elastic Systems , 1965 .

[2]  H. Troger,et al.  Nonlinear stability and bifurcation theory , 1991 .

[3]  H. Ziegler,et al.  Linear elastic stability , 1953 .

[4]  V K Garg,et al.  Dynamics of railway vehicle systems , 1984 .

[5]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[6]  Peter Hagedorn,et al.  On the destabilizing effect of non-linear damping in non-conservative systems with follower forces , 1970 .

[7]  A. S. Vol'mir.  Stability of elastic systems , 1965 .

[8]  On the motion of a reversible double simple pendulum with tracking force , 1999 .

[9]  R. Plaut.  A New Destabilization Phenomenon in Nonconservative Systems , 1971 .

[10]  Y. Matsuzaki,et al.  Bifurcations in a two-degree-of-freedom elastic system with follower forces , 1988 .

[11]  Existence of periodic motions of dynamic systems with simple symmetry , 1997 .

[12]  C. P. Keizer.  INTRODUCTION TO THE DYNAMICS OF RAIL VEHICLES , 1987 .

[13]  R. Scheidl,et al.  Coupled flutter and divergence bifurcation of a double pendulum , 1984 .

[14]  V. V. Bolotin,et al.  Nonconservative problems of the theory of elastic stability , 1963 .

[15]  Stability of equilibrium for an inverted two-link mathematical pendulum with critical tracking forces , 1999 .

[16]  Generalization of the rayleigh theorem to gyroscopic systems: PMM vol. 40, n≗ 4, 1976, pp. 606–610 , 1976 .

[17]  F. Dimentberg.  Flexural vibrations of rotating shafts , 1961 .

[18]  Kurt Magnus.  Der Einfluß verschiedener Kräftearten auf die Stabilität linearer Systeme , 1970 .

[19]  Junfeng Li.  On the stability of dissipative mechanical systems with circulatory forces , 1997 .

[20]  S. Otterbein.  Stabilisierung des n-Pendels und der Indische Seiltrick , 1982 .

[21]  Y. Matsuzaki,et al.  Stability and bifurcations of a double pendulum subjected to a follower force , 1989 .

[22]  Character of motion of oscillating pendulum systems at the boundary of the stable region , 1999 .

[23]  H. Troger,et al.  Zur korrekten Modellbildung in der Dynamik diskreter Systeme , 1981 .

[24]  Steady-state manifolds of a wheeled vehicle with an asymmetrically positioned center of mass , 1998 .

[25]  L. G. Lobas.  On rolling systems , 2000 .