Abstract We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on simplest possible dynamical structure provided by Keplerian problem perturbed resonant coupling truncated at second order eccentricities. reduced Hamiltonian, constructed transformation to coordinates, then submitted suitable ordering of terms and study its equilibria. Henceforth, n...

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...