Conversion of equation which preserves motion

[shethroh]

Hi,

Well I would like to know if we can change equation such that the relation between independent and dependent variable will be same but has some different form.

Let me explain it:

For eg. ψ(t)=-3-43cos(ω*t), is a periodic function. Now when you differentiate it with respect to time the constant term is lost.

I would like to know if we can somehow change equation such that the constant term is not lost in differentiation, and also the relationship between ψ and time is preserved.

 

[chiro]

Hey shethroh and welcome to the forums.

For For ψ(t)=-3-43cos(ω*t), if you want the relationship preserved then you can't do what you want to do.

If you end up modifying your equation to get something like ψ(t)=-3t-43cos(ω*t) then it will be completely different. Basically instead of being periodic, the centre of each wavelength will drift towards negative infinity as time goes on: in other words it won't resemble anything like the previous function in its behaviour.

Just out of curiosity, why do you want to do this? Is there any reason or application you had in mind? If there is, it might help if you posted it on here for the rest of us to look at and comment on.

 

[shethroh]

Thanks for your answer.

Well I am doing a fluid dynamics simulation on a software where body is in motion. Therefore I need to input the angular velocity to the software, which is derivative of the above angle I have mentioned. But the motion I get is not desired, therefore the support team of software suggested me to input the angular velocity such that the constants are preserved from the equation.

The equation that you have given, in that you multiplied constant with t but is there some way by which we can convert/transform the equation?

Hey shethroh and welcome to the forums.

For For ψ(t)=-3-43cos(ω*t), if you want the relationship preserved then you can't do what you want to do.

If you end up modifying your equation to get something like ψ(t)=-3t-43cos(ω*t) then it will be completely different. Basically instead of being periodic, the centre of each wavelength will drift towards negative infinity as time goes on: in other words it won't resemble anything like the previous function in its behaviour.

Just out of curiosity, why do you want to do this? Is there any reason or application you had in mind? If there is, it might help if you posted it on here for the rest of us to look at and comment on.

 

[chiro]

It would help if you gave the form of your function in its most abstract nature relevant for your problem as well as the derivative (you could specify one or the other or even both to show a contradiction between the two if they are incompatible).

This way we can prove whether a derivative exists in the form that it should or show that a contradiction occurs for either the derivative, the function or both.

 

[shethroh]

It would help if you gave the form of your function in its most abstract nature relevant for your problem as well as the derivative (you could specify one or the other or even both to show a contradiction between the two if they are incompatible).

This way we can prove whether a derivative exists in the form that it should or show that a contradiction occurs for either the derivative, the function or both.

Thanks a lot man for your help, but I didn't require to convert equation. But because I have asked here let me clear what was it about. The equation was obtained from experiments done over flapping wings by Fourier expansion. The equation defined how the flapping angle of wings changed with time, and in software I needed to put the (dψ/dt).

Thanks again chiro.