Stability Analysis of Relative Equilibria of Mechanical Systems with Cyclic Coordinates
W. Steiner - Stability Analysis of Relative Equilibria of Mechanical Systems with Cyclic Coordinates - ARCHIVE OF APPLIED MECHANICS, Vol. 2006, No. 75, 2006, pp. 355-363
Nonlinear stability of relative equilibria of mechanical systems has been investigated during the
past two decades by notable authors and has resulted in the so-called energy momentum method. Although of numerous important engineering applications this theory involves subtle mathematical methods such as group theory to which engineers usually are not familiar. This paper develops a simple and natural approach to the
problem for the case of cyclic coordinates in the Lagrangian since many practical examples can be easily formulated in terms of cyclic coordinates. Referring to standard algebraic operations a stability criterion for relative equilibria is derived. As a computational benefit the presented approach does not require to know the system’s complete kinetic energy, neither for formulating steady state equations nor for checking stability. The application of the method which is closely related to Routh’s method will be demonstrated by the example of a dumbell satellite.