Timeline for Coupled Riccati equations
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 22, 2023 at 13:18 | comment | added | silmar | Thank you. Finally I could reproduce this last result. However, when we replace the expression for r (r=h(theta)), derived from this last equation, in rd(theta)/dt = g(theta), yielding h(theta)d(theta)/dt = g(theta), we end up with an integral (in theta) which has no primitive in terms of elementary functions, right ? | |
| Mar 15, 2023 at 14:26 | comment | added | მამუკა ჯიბლაძე | @silmar I get (up to a constant)$$\ln(r)=\frac{b^2-a_1a_2}{(b-a_1)(b-a_2)}\ln\left(a_1(b-a_2)\sin(\theta)-(b-a_1)a_2\cos(\theta)\right)\qquad-\frac{a_1}{b-a_1}\ln\sin(\theta)-\frac{a_2}{b-a_2}\ln\cos(\theta)$$ | |
| Mar 11, 2023 at 1:09 | comment | added | silmar | Abel, just one more short question: From a closer look I think that the integral in theta doesn't have a primitive. What do you think ? Thank you again. | |
| Mar 10, 2023 at 23:54 | comment | added | silmar | Dear Abel,Thank you very much for your answer. Now I am trying to figure out how to solve the integral involving theta. | |
| Mar 10, 2023 at 3:38 | history | edited | Michael Engelhardt | CC BY-SA 4.0 |
fixed bracket typo
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| Mar 10, 2023 at 1:19 | history | answered | abel | CC BY-SA 4.0 |