as said in the title I have different results between numerical en vector approach during inclination changing maneuver.
The initial orbit :
Perigee radius : 6700 km
Eccentricity : 0.7
Inclination : 40.0 °
Ascending node : 20.0 °
Perigee Argument :10.0 °
The target orbit is the same with inclination set at 55 °, so we have a relative inclination of 15°
My vector approach:
At planes intersection I subtract final vector by initial vector and I get the following result : |delta_v| = 2608.9 m/s
And the result of my new orbit matches perfectly all expected parameters.
Now the problem comes from the numerical approach :
I compute delta v magnitude |delta_v| = 2.0 * velocityAtNode * sin(relativeInclination * 0.5) = 2615,65 m/s
My delta v vector is initialized on normalized velocity vector.
I compute the rotation amplitude of my normalized delta v vector : rotationAngle = 90° + relativeInclination*0.5; = 97.5 °
I rotate my normalized delta V vector around line of nodes axis by an angle of 97.5°
Then I apply delta v computed previously to my rotated normalized vector: final delta v vector = rotated normalized vector * 2615,65
I add this delta v vector to my initial velocity vector
In this numerical approach the orbits planes are perfectly aligned but I've a drift in others parameters :
perigee height becomes : 6675 km
eccentricity : 0.706
perigee argument : 12°
If I compare my delta v vector obtained by vector approach and by numerical approach. I notice an angle of 4.1° between these two vectors and a magnitude difference of 6.7 m/s
Any help is welcome to understand the difference between these two approaches. Thanks!