I was reading Hollister David's short paper on bi-tangential transfers. The example he uses is a transfer between a planar circular and an elliptical orbit. I am wondering: Is an ideal, that is, the lowest $\Delta v$ cost, transfer between two arbitrary orbits around a single point mass always an ellipse that is tangential to both the orbits? I am excluding the cases where a bi-elliptical transfer is ideal, as the answer is then always a manoeuvre with infinite apoapsis.
I am not entirely comfortable with trusting that as a safe assumption, as although paying a $\Delta v$ expense in another direction than prograde or retrograde is expensive, it is by no means horrible. If this assumption is indeed not true, what criteria must to planar arbitrary orbits satisfy in order to make the ideal transfer between them a bi-tangential ellipse?
A transfer orbit being "tangential" to an orbit means that in the transition between the orbit and the transfer orbit, velocity change is only applied in the prograde or retrograde direction. A "bi-tangential transfer" is when the transfer orbit between a pair of orbits is tangential to both of them. As a consequence, this problem is strictly planar. The "bi-elliptical transfer" I am referring to is when the alternative with the lowest cost is to do a burn at periapsis accelerating to infinity, then performing zero-cost manoeuvres "at infinity" before falling back to the other orbit's periapsis.
Example of a bi-tangential transfer. Both burns are done tangentially:
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