Distribution (Dirac&standard) formulations of f=ma how do they go again?

[James MC]

F = dp/dt is just a shorthand form of three separate equations containing different component of force. Parallel and perpendicular components of force are just one among many equally valid ways to write these three equations.

What do you mean by "direction relative properties of inertia L"? If you mean by it the ratio of force and acceleration in the same direction, then yes, this follows from that equation.

That is what I mean. I just don't understand how it follows.

If F=dp/dt is just shorthand for three separate equations for each component of force, then F=dp/dt entails that there is nothing special about one particular component. [ii] But there is something special about the component that is parallel to the velocity: there is more inertia in that direction.

This argument against F=dp/dt contains only two premises, and [ii], and is clearly valid. So either or [ii] (or both) is false?

 

[Jano L.]

F - dp/dt give no component a distinct behaviour, but p = gamma m v does.

 

[MikeGomez]

That is what I mean. I just don't understand how it follows.

If F=dp/dt is just shorthand for three separate equations for each component of force, then F=dp/dt entails that there is nothing special about one particular component. [ii] But there is something special about the component that is parallel to the velocity: there is more inertia in that direction.

This argument against F=dp/dt contains only two premises, and [ii], and is clearly valid. So either or [ii] (or both) is false?

James, it gets worse. Align the force/change in momentum with the x-axis. Now the entire effect is in the direction of the x component, and ther is no effect in the y or z componnents!