Superposition of position functions

In summary, the conversation discusses the relationship between two forces, F_1 and F_2, acting on a body 'a' and how it affects its position over time. It is determined that the position of 'a' is given by two position vectors, r_1(t) when only F_1 acts and r_2(t) when only F_2 acts. However, when both forces act on the body, the resulting position is given by r_c. The question is whether the relation r_c = r_1 + r_2 always holds true, and it is stated that it may not in cases such as rigid body rotation, nonlinear optics, and fluid flow. It is then confirmed that the principle of superposition
  • #1
rohanprabhu
414
2
If I have two forces, [itex]F_1[/itex] and [itex]F_2[/itex], such that, if a body 'a' is applied only one of the two forces, either [itex]F_1[/itex] and [itex]F_2[/itex] for a given experiment and it is determined that.. if only [itex]F_1[/itex] acts on 'a', then the position of 'a' is given by: [itex]r_1(t)[/itex] where '[itex]r_1[/itex]' is a position vector as a function of time and if only [itex]F_1[/itex] acts on 'a', then the position of 'a' is given by [itex]r_2(t)[/itex], where '[itex]r_2[/itex]' is a position vector as a function of time.

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

[tex]
r_c = r_1 + r_2
[/tex]
 
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  • #2
Surely that is not always the case: rigid body rotation, nonlinear optics, fluid flow...
 
  • #3
Yes, the principle of superposition is applicable in this case. Of course, once your system becomes non-linear, then it no longer holds.

Claude.
 

Related to Superposition of position functions

What is superposition of position functions?

Superposition of position functions is a concept in physics where the position of an object is described by combining the individual position functions of each component of the object.

How does superposition of position functions work?

To use superposition of position functions, you must first determine the individual position functions for each component of the object. Then, you add these functions together to get the overall position function for the object.

What is the purpose of using superposition of position functions?

Superposition of position functions is used to describe the position of complex objects that are made up of multiple components. It allows us to understand the overall motion of the object by breaking it down into simpler components.

What is the difference between superposition of position functions and superposition of waves?

Superposition of position functions deals with the position of objects, while superposition of waves deals with the amplitude and phase of waves. However, both concepts use similar principles of combining individual functions to describe a larger system.

Can superposition of position functions be applied to objects in real life?

Yes, superposition of position functions is a fundamental concept in physics and is applied in various fields such as mechanics, electricity and magnetism, and quantum mechanics. It can be used to describe the motion of objects such as planets, particles, and even waves.

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