Exploring the Restricted Three Body Problem: Hamiltonian vs Lagrangian Approach

I am having a difficult time finding papers that derive the equations of motions of the Restricted Three Body Problem using Newtonian mechanics. I have found some (barely) for the CRTBP, but there are none on the ERTBP.

Does it depend on what is being studied within the problem that the Hamiltonian approach is the preferred?Thank you!

The Hamiltonian or Lagrangian approach is used because its simpler dealing only with the energies of the system.

The Newtonian method is far harder to setup properly.There's a fair amount of labeling and keeping track of postions, momentum and forces.

Here's a video where the presenter uses Newtonian methods initially:




and uses python to simulate the system.

In contrast, this presenter uses the Lagrangian methods: