ABSTRACT
We show that for symmetric mechanical systems, no matter whether they are dissipative or Hamiltonian, it is of great advantage to make use of the symmetry properties when solving stability problems. As a model problem for a dissipative dynamical system, the loss of stability of the trivial downhanging equilibrium position of a slender circular tube conveying incompressible fluid flow is studied. Application of the methods of equivariant bifurcation theory show that without ex-tensive use of symmetry properties the treated problem hardly could be solved. For the Hamiltonian case we study the stability of relative equilibria of a dumbbell satellite, explaining the reduced energy momentum method which, relying on symmetry properties of the Hamiltonian and conserved quantities, simplifies the solution of the problem considerably.
