Superposition of position functions

[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:

<br /> r_c = r_1 + r_2<br />

 

[Andy Resnick]

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

 

[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.