# Superposition of position functions

1. Feb 28, 2008

### rohanprabhu

If I have two forces, $F_1$ and $F_2$, such that, if a body 'a' is applied only one of the two forces, either $F_1$ and $F_2$ for a given experiment and it is determined that.. if only $F_1$ acts on 'a', then the position of 'a' is given by: $r_1(t)$ where '$r_1$' is a position vector as a function of time and if only $F_1$ acts on 'a', then the position of 'a' is given by $r_2(t)$, where '$r_2$' is a position vector as a function of time.

Now, the body is subjected to both the forces $F_1$ and $F_2$ and the position of 'a' is given is by $r_c$. Then, does this relation hold true:

$$r_c = r_1 + r_2$$

2. Feb 28, 2008

### Andy Resnick

Surely that is not always the case: rigid body rotation, nonlinear optics, fluid flow...

3. Feb 28, 2008

### Claude Bile

Yes, the principle of superposition is applicable in this case. Of course, once your system becomes non-linear, then it no longer holds.

Claude.