Atmospheric reentry, as I understand it, is a balancing act between minimizing delta-v needed and not burning up or breaking up in the atmosphere. The higher the velocity on reentry, the greater the reentry heating and aerodynamic forces experienced by the vehicle. Of course, if you had all the delta-v in the world, you could use repeated burns to minimize velocity all the way down to the ground, but to better understand a real-world model, I'm curious about the optimal non-propulsive trajectory (as in "pick a velocity and drop") from low-earth orbit (any inclination will do, but preferably at least mention the case of an equatorial orbit) to sea level.
Of all possible non-propulsive deorbit and reentry trajectories from LEO, which one minimizes total reentry heating and aerodynamic forces? Notably, there may be different trajectories to minimize each of total reentry heating and aerodynamic forces, so I separated them and tried to use the Euler equation to minimize the Euler equations*, but that didn't get me anywhere as I ended up with nonsensical differential equations.
If someone happens to know the optimal trajectory(ies) to minimize reentry heating and aerodynamic forces, preferably but not necessarily with some mathematical backing, please let me know :)
* Hehehehe, I mean using the Euler-Lagrange equation to minimize a functional derived from the Euler equations for adiabatic flow, incredible to me that Leonhard did all of this back in the 1700s