Newton's Second Law and Inertial Frames Of Refence

[cwstrick]

I have a question about Newton's Second Law and Inertial Frames of Refrence. It is canon that Newton's Second Law is only applicable in an inertial frame of refrence. Newton's Second Law is the net force acting on a body is equal to the time rate of change of the body's linear momentum. Expressed mathematically N.S.L is

$$\sum$$ F = dp/dt = d(mv)/dt = (dm/dt)v + m(dv/dt)

Lets define a general velocity vector using arbitrary coordinates.The Einstein Summation Convention is being used. Let v = v^ae_a
then (dv/dt) = (dv^a/dt)e_a + v^a(de_a/dt). Substituting this into the equation above and factoring one can arrive at

$$\sum$$ F = [(dm/dt)v^a + m(dv^a/dt)]e_a + mv^a(de_a/dt).

In regular cartesian coordinates, the last term in zero. My question is, can one apply N.S.L. in an accelerating frame of refrence by adding the last term, mv^a(de_a/dt), instead of adding ficticious forces?

 

[Dale]

That last term probably is the fictitious force. Try it with a standard non-inertial frame like a rotating or uniformly accelerating system and see.