The Lynden-Bell bar formation mechanism in simple and realistic galactic
  models
  Using the canonical Hamilton-Jacobi approach we study the Lynden-Bell concept
of bar formation based on the idea of orbital trapping parallel to the long or
short axes of the oval potential distortion. The concept considered a single
parameter - a sign of the derivative of the precession rate over angular
momentum, determining the orientation of the trapped orbits. We derived a
perturbation Hamiltonian which includes two more parameters characterising the
background disc and the perturbation, that are just as important as the earlier
known one. This allows us to link the concept with the matrix approach in
linear perturbation theory, the theory of weak bars, and explain some features
of the nonlinear secular evolution observed in N-body simulations.
