YES:- You are missing some thing.

Mathematical derivatives always contain variables as it is applicable to all parameters & conditions.

In above example, I prove that in post 4 or in post 13 that in single frame analysis or in two relative frame analysis.

Even there is no force is applied in X-direction then also relativity create mathematical non-applied force in x-direction.

So, effect is applied force is different than acting force.

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In Post 13, I prove that if we do not consider that non-applied horizontal force in to the mathematical calculation then d'E=dEo/y, d'M=dMo/y

if we do consider that non-applied horizontal force in to the mathematical calculation then only d'E=y dEo, d'M=y dMo

Means, non-applied mathematical horizontal force is responsible for d'E=y dEo, d'M=y dMo

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Means, If Bomber drop the Bomb Mo kg moving with horizontal velocity

then for Observer on ground actual force acting is gravitational force but relativity create the mathematical horizontal force.

If we do not consider non-applied horizontal force then d'E=y dEo, d'M=y dMo is wrong.

This horizontal force is created due to vertical acceleration & horizontal velocity

I think I get what you saying finally. I think what you need to look at is frame dragging: https://en.wikipedia.../Frame-dragging

I think that is the x direction force?