According to (Burt, 1967)[1], the transverse component of the perturbing force (that is: contained in the plane of the orbit and perpendicular to the radius vector) is the only one that affects secular changes of both the semimajor axis and the eccentricity (eqs. (17) and (15)):
$$ \widetilde{\frac{\operatorname{d}\!a}{\operatorname{d}\!t}}=\frac{2 a^{3/2}}{\mu^{1/2}} \left(1 - e_0^2 \left( \frac{a_0}{a}\right)^{3/2} \right)^{1/2} f_2 $$
$$ \widetilde{\frac{\operatorname{d}\!e}{\operatorname{d}\!t}}=-\frac{3}{2} \left(\frac{p}{\mu}\right)^{1/2} e f_2 $$
On the other hand:
Later in the same paper it's stated that tangential thrust $f_T$, which is effectively a combination of radial $f_1$ and transverse $f_2$ thrust, "leads to a slightly more rapid enlargement of the orbit".
It is well known that the quasi-optimal strategy for eccentricity change involves exerting thrust along a inertially fixed direction in space perpendicular to the semimajor axis (Edelbaum 1961, Pollard 1997, Ruggiero 2011). Moreover, (Pollard, 1997)[2] states that the secular variation of the eccentricity with such a program is
$$ \left|\widetilde{\frac{\operatorname{d}\!e}{\operatorname{d}\!t}}\right|=\frac{3}{2} f \sqrt{\frac{a}{\mu}} \sqrt{1 - e^2} $$
which is very close to the Burt result except for an $e$ factor.
How do these results not contradict the fact that only transverse $f_2$ thrust produce secular changes on semimajor axis $a$ and eccentricity $e$? If $f_2$ is the only component producing secular changes, shouldn't the radial component present in $f_T$ and the inertially fixed thrust program be immaterial to the evolution of $a$ and $e$?
[1]: Burt, E. G. C. "On space manoeuvres with continuous thrust." Planetary and Space Science 15.1 (1967): 103-122.
[2]: Pollard, James E. "Simplified approach for assessment of low-thrust elliptical orbit transfers." 25th International Electric Propulsion Conference, Cleveland, OH. 1997.
