[montecarl]

Thermostats ensure that the average _kinetic energy_ remains constant (on average or instantaneously depending on how they are implemented). Your parent post wants to enforce the constraint that the total energy remains constant. So its a bit different from a canonical ensemble (NVT) simulation. This is a microcanonical ensemble simulation (NVE). This means you don't know if you should correct the position (controlling the potential energy) or the velocities (controlling the kinetic energy).

Basically, there will be error in the positions and velocities due to the integrator used and you don't know how to patch it up. You have 1 constraint; the total energy should be constant. There are 2(3N-6) degrees of freedom for the positions and velocities (if more than 2 bodies). The extra constraint doesn't help much!

Edit: Also, the only reason thermostats work is because the assumption is that the system is in equilibrium with a heat bath (i.e. bunch of atoms at constant temperature). So there is an entire distribution of velocities that is statistically valid and as long as the velocities of the atoms in the system reflect that, you will on average model the kinetics of the system properly (e.g. things like reaction rates will be right). In gravitational problems there is no heat bath.