On degenerate integrable hamiltonian systems

Is there some reference where the existence of local generalized action-angle variables is discussed in some detail for concrete examples of hamiltonian systems of mechanical type?

After Dazord and Delzant, by local generalized action-angle coordinates on a symplectic manifold $(M^{2n},\omega)$ I mean a locally trivial bundle $\pi:M\to P$ with fiber $\mathbb{T}^k$ and having a trivializing atlas whose elements $(U,\phi:\pi^{-1}(U)\to U\times\mathbb{T}^k)$ satisfy the following property:
$\phi_{\ast}\omega=\sum_{i=1}^k dJ_i\wedge \theta_i+\sum_{i=1}^{n-k}dp_i\wedge dp_i$ where $J_1,\ldots,J_k,p_1,\ldots,p_{n-k},q_1,\ldots,q_{n-k}$ are adapted coordinates on $U$ and $\theta_1\ldots,\theta_k$ is a base of invariant $1$-forms on $\mathbb{T}^k$.

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How about the book "Global Aspects of Classic Integrable Systems" by Cushman and Bates? it is concerned with monodromy and the global existence of action-angle coordinates, so I'm pretty sure it does a good job of sketching the local picture, although I don't have a copy with me right now. –  jvkersch Jun 21 '11 at 22:29
Dear jvkersch, thank you for the reference. Even if in this book there is no mention of degenerate (or super, non commutative) integrability, the detailed analysis of the topology of the momentum map for many classical ham. systems ( Euler top, kepler problem, harmonic oscillator,...; that, by the way, are superintegrable) should permit to recognize the existence of generalized action-angle coordinates at least on a open subset of the phase space. –  Giuseppe Tortorella Jun 23 '11 at 6:32