Finding a solution for Relativistic Acceleration

[Michio Cuckoo]

I tried all my mathcad software such as Maple and I can't seem to find a solution to this time based differential equation.

 

[JJacquelin]

I tried all my mathcad software such as Maple and I can't seem to find a solution to this time based differential equation.

Hi !

Very surprising ! They should solve this EDO without any difficulty, since it is an EDO of the "separable variables" kind. This can be handly carried out.

 

[jackmell]

I tried all my mathcad software such as Maple and I can't seem to find a solution to this time based differential equation.

Whenever you have a messy-looking equation, it's sometimes helpful to at least initially, get rid of all the fluff by canonicalizing the equation. In the case above, write it simply as:

$$\frac{dy}{dt}=k(1-y^2/a)^{3/2}$$

See, just that lil' bit is good progress. Now, you can't separate variables and integrate? Telll you what, can you integrate just:

$$\int \frac{dy}{(1-y^2/a)^{3/2}}$$

I haven't tried so I don't know. You try it.

 

[hunt_mat]

This might be a two stage process, first try a substitution of $y=\sqrt{a}\sin\theta$ and see what you get.

 

[blue_raver22]

I understand the frustration of not being able to find a solution to a complex problem like Relativistic Acceleration. However, it is important to remember that not all problems have a straightforward solution and sometimes, it takes multiple attempts and different approaches to find a solution. It may be helpful to collaborate with other scientists or seek advice from experts in the field to gain new perspectives and insights on the problem. Additionally, it may be beneficial to continue exploring different mathematical software and techniques to see if any of them can provide a solution. Persistence and perseverance are key qualities in scientific research, and I am confident that with determination and an open mind, a solution to this problem can be found.