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 $\mathbb{T}^k$.