  Gauge invariance of scalar perturbations is studied together with the
associated equations of motion. Extending methods developed in the framework of
hamiltonian General Relativity, the Hamilton-Jacobi equation is investigated
into the details in Loop Quantum Cosmology. The gauge-invariant observables are
built and their equations of motions are reviewed both in Hamiltonian and
Lagrangian approaches. This method is applied to scalar perturbations with
either holonomy or inverse-volume corrections.
