TY - JOUR

T1 - Stability Analysis of Relative Equilibria of Mechanical Systems with Cyclic Coordinates

T2 - A direct approach

AU - Steiner, Wolfgang

PY - 2006/3

Y1 - 2006/3

N2 - 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 it has numerous important engineering applications, this theory involves subtle mathematical methods such as group theory with 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 knowledge of a system's complete kinetic energy, either for formulating steady-state equations or for checking stability. The application of the method, which is closely related to Routh's method, will be demonstrated using the example of a dumbell satellite.

AB - 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 it has numerous important engineering applications, this theory involves subtle mathematical methods such as group theory with 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 knowledge of a system's complete kinetic energy, either for formulating steady-state equations or for checking stability. The application of the method, which is closely related to Routh's method, will be demonstrated using the example of a dumbell satellite.

KW - Cyclic coordinate

KW - Dumbell satellite

KW - Nonlinear mechanical system

KW - Reduced energy momentum method

KW - Relative equilibrium

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=33644583621&partnerID=8YFLogxK

U2 - 10.1007/s00419-005-0428-z

DO - 10.1007/s00419-005-0428-z

M3 - Article

SN - 0939-1533

VL - 75

SP - 355

EP - 363

JO - Archive of Applied Mechanics

JF - Archive of Applied Mechanics

IS - 6-7

ER -