Changing Origin in Physical Context: Mathematical Approach

[qwop]

In a general situation, how do you change origin (mathematically speaking) in a physical context i.e. with position vectors, constant vectors, unit vectors to certain directions ... ?

I am a bit confused with the concept.

 

[Emissive]

If You have a Cartesian co-ord system of x, y, z with origin set at 0,0,0 then you need to add or subtract from the x, y, z of the function by the amount you are moving the origin.

Ie if y=3x at origin x0,y0 then at a new origin x4,y3 the function will be y+3=3x+4 or y=3x+1.

 

[qwop]

So if I have an equation x'=(x(cross)n)+a
where x is the position vector, x' time derivative, n unit constant, a constant, then I get changing by x->x+c:
(x+c)'=((x+c)(cross)(n+c))+(a+c)
is this what you meant?