- #1
Michio Cuckoo
- 84
- 0
I tried all my mathcad software such as Maple and I can't seem to find a solution to this time based differential equation.
![m}\left%20(%201%20-%20\frac{\left%20[%20f(t)%20\right%20]^{2}}{c^{2}}%20\right%20)^{\frac{3}{2}}.gif](https://www.physicsforums.com/attachments/m-left-20-201-20-20-frac-left-20-20f-t-20-right-20-2-c-2-20-right-20-frac-3-2-gif.153032/ "m}\left%20(%201%20-%20\frac{\left%20[%20f(t)%20\right%20]^{2}}{c^{2}}%20\right%20)^{\frac{3}{2}}.gif")
Finding a solution for Relativistic Acceleration
- Context: Graduate
- Thread starter Michio Cuckoo
- Start date
-
- Tags
- Acceleration Relativistic
Click For Summary
Discussion Overview
The discussion revolves around finding a solution to a time-based differential equation related to relativistic acceleration. Participants explore various mathematical approaches and techniques to tackle the problem, including canonical forms and substitutions.
Discussion Character
- Technical explanation, Mathematical reasoning, Debate/contested
Main Points Raised
- One participant expresses difficulty in solving the differential equation using software like Maple, suggesting it should be solvable as it is of the "separable variables" type.
- Another participant agrees that the equation can be handled and suggests canonicalizing it to simplify the problem.
- A different participant proposes integrating a specific form of the equation and encourages others to attempt the integration.
- Another suggestion involves using a substitution method, specifically y=\sqrt{a}\sin\theta, to facilitate the solution process.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the solution method, with multiple approaches being proposed and no clear agreement on the best path forward.
Contextual Notes
There are unresolved mathematical steps and assumptions regarding the methods proposed, particularly concerning the integration and substitution techniques.
- #2
JJacquelin
- 801
- 35
Michio Cuckoo said:I tried all my mathcad software such as Maple and I can't seem to find a solution to this time based differential equation.
![m}\left%20(%201%20-%20\frac{\left%20[%20f(t)%20\right%20]^{2}}{c^{2}}%20\right%20)^{\frac{3}{2}}.gif](https://www.physicsforums.com/attachments/m-left-20-201-20-20-frac-left-20-20f-t-20-right-20-2-c-2-20-right-20-frac-3-2-gif.153035/ "m}\left%20(%201%20-%20\frac{\left%20[%20f(t)%20\right%20]^{2}}{c^{2}}%20\right%20)^{\frac{3}{2}}.gif")
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.
- #3
jackmell
- 1,806
- 54
Michio Cuckoo said:I tried all my mathcad software such as Maple and I can't seem to find a solution to this time based differential equation.
![m}\left%20(%201%20-%20\frac{\left%20[%20f(t)%20\right%20]^{2}}{c^{2}}%20\right%20)^{\frac{3}{2}}.gif](https://www.physicsforums.com/attachments/m-left-20-201-20-20-frac-left-20-20f-t-20-right-20-2-c-2-20-right-20-frac-3-2-gif.153040/ "m}\left%20(%201%20-%20\frac{\left%20[%20f(t)%20\right%20]^{2}}{c^{2}}%20\right%20)^{\frac{3}{2}}.gif")
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:
[tex]\frac{dy}{dt}=k(1-y^2/a)^{3/2}[/tex]
See, just that lil' bit is good progress. Now, you can't separate variables and integrate? Telll you what, can you integrate just:
[tex]\int \frac{dy}{(1-y^2/a)^{3/2}}[/tex]
I haven't tried so I don't know. You try it.
Last edited:
- #4
hunt_mat
Homework Helper
- 1,816
- 33
This might be a two stage process, first try a substitution of [itex]y=\sqrt{a}\sin\theta[/itex] and see what you get.
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