- #1
Intesar
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- Homework Statement
- I came across these equations in a mechanics textbook and wish to differentiate the first equation w.r.t. time to obtain that second equation. Any help is much appreciated!
$$c(f_1+f_2)=a^2(\frac{1}{2}\dot{a}^2 -ca+h)+2af'_2$$
$$c(1-\frac{\dot{a}}{c})(f'_1+f'_2)=ca(-2\dot{a}^2 (1-\frac{1}{2}\frac{\dot{a}}{c})-a\ddot{a}(1-\frac{\dot{a}}{c})+2\frac{\dot{a}}{c}h+\frac{a}{c}\dot{h})+2a(1+\frac{\dot{a}}{c}){f''_2}$$
##f_1(x)=f_1(t-\frac{r}{c})##, ##f_2(x)=f_2(t+\frac{r}{c})##
The book didn't explicitly state the functions of time, but from the second equation we can see that ##a## and ##h## are functions of time.
We also know that $$\frac{f'_1+f'_2}{a}+\frac{1}{2}\dot{a}^2+h=0$$ (if that's of any help)
- Relevant Equations
- Please see above
I tried doing it a few times and this is all I get:
Please let me know where I'm going wrong. Thanks
c(˙f1+˙f2)=a˙a2+a2˙a−3ca2+˙ha2+2ha+2˙af′2+2a˙f′2c(f1˙+f2˙)=aa˙2+a2a˙−3ca2+h˙a2+2ha+2a˙f2′+2af2′˙
Please let me know where I'm going wrong. Thanks
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