# Integrate vector in rotating frame?

1. Jan 6, 2012

### Hare

Hi.
Ok, so I'm trying to understand the "navigation equations".

n: frame traveling on earth with vehicle.
e: frame centered in earth, rotating with it.
P: Position of vehicle center of gravity.

v$^{n}_{P/e}$ = (vn,ve,vd): velocity of P w.r.t to e-frame, expressed in n-frame.

Normally you don't integrate this, but uses vn,ve,vd to calculate the derivative of longitude,latitude,height and then integrate these to get position in longitude,latitude,height.

BUT, my question is: what do you get if you integrate vn,ve,vd?

I mean, normally when you integrate vectors:
- the frame is fixed in space
- you have a velocity w.r.t this frame
- and you just integrate each component separately

But now
- the frame is rotating
- velocity is not w.r.t this frame

Any thoughts?

/Jonas

2. Jan 6, 2012

### RCP

Bump. My only thought is I so wish some of the cognoscenti here would comment on your questions Hare. I suspect perhaps a few are brave enough to jump into this rabbit warren with no visible bottom. Certainly not I, but some answers here might be helpful on a related subject. Anyone?