Recursive function in a physics equation

In summary: Ok. Thank you for your help. In summary, fractals are recursive structures that are often generated by recursive algorithms.
  • #1
noize11
3
0
Hoping someone can point out an example of a recursive function in a physics equation. If this is not a valid step that would be great to hear about too. Also if anyone has even tried to introduce such an equation in the past or how it might be represented. [I'm not the best student of maths].

I have a form in mind that I can only express with recursion.


Thanks in advance.
 
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  • #2
What do you mean by recursion? Is it of the form:
[itex]
x_{n+1} = f(x_n)
[/itex]
or is it something like
[itex]
y = f(y)
[/itex]
where f(y) is some nasty integral or something which you can't solve?

In either case, yes, recursion occurs a lot in physics and is the basis for things like perturbation theory.

Matt
 
  • #3
Something more along these lines:

[tex] v(t) = 3 * v(t) [/tex]

Obviously this equation cannot be solved as there is no terminating condition specified. Trying to solve this when t=1 for instance gives:

[tex] v(1) = 3* (3* (3 * (3 * (3* ...))))[/tex]

I have a structure that relies on this form of recursion, but how do I go about specifying the terminating value? For instance, suppose I simply wanted a value > 8 * PI. How is it that I would express this?
 
  • #4
Hmm, either something fishy is going on or you need help from a mathematician (which sadly I'm not).

By my reconing the only 'physical' solution to your equation is zero. My argument would run as follows:

Assume [itex]v(t)[/itex] has a solution [itex]v(t)>0[/itex].

[itex] v(t) = 3 v(t) \Rightarrow 1 = 3[/itex]
This is a contradiction hence [itex]v(t)=0[/itex].

Unless I am wrong in thinking your symbol [itex]*[/itex] means multiply?

Ok, as I said before I am not a mathematician so if I've done something stupid please don't hurt me :)

Matt
 
  • #5
Would you like to explain better what you are trying to do. It is interesting your topic and please give us details. I really don't know what to say about your recursive physics, but I ran into similar ideas, too. Maybe I can help :)
 
  • #6
fractals

BreAkeR said:
Would you like to explain better what you are trying to do. It is interesting your topic and please give us details. I really don't know what to say about your recursive physics, but I ran into similar ideas, too. Maybe I can help :)

Aren't fractals recursive?
 
  • #7
mee said:
Aren't fractals recursive?

If by that you mean a great many of them are generated by recursive algorithms, then yes they definitely are.

Matt
 

1. What is a recursive function in a physics equation?

A recursive function in a physics equation is a mathematical function that is defined in terms of itself. This means that the function is computed repeatedly using its own output as an input, creating a loop or "recursion".

2. How is a recursive function used in physics?

Recursive functions can be used to solve complex problems in physics, such as calculating the position or velocity of an object over time. They can also be used to model natural phenomena, like the growth of a population or the behavior of a pendulum.

3. Are there any limitations to using recursive functions in physics?

Recursive functions can be difficult to solve and can sometimes lead to infinite loops if not carefully designed. They also require a lot of computational power, so they may not be practical for all physics problems.

4. Can you provide an example of a recursive function in a physics equation?

An example of a recursive function in a physics equation is the formula for calculating the position of an object at a given time t, given its initial position (x0) and velocity (v0): x(t) = x0 + v0t + ½at2. This function uses the position at the previous time step to calculate the position at the current time step, making it recursive.

5. How do you know when to use a recursive function in a physics equation?

Recursive functions are typically used when a problem requires a repetitive calculation or when the solution is dependent on previous steps. They can also be used to solve problems that have a self-similar structure, such as fractals or patterns in nature.

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