Timeline for Intercept the missile
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 19, 2020 at 13:24 | comment | added | Timothy Budd | There is no $\epsilon/t$ in the integral in the two-dimensional case. The excluded length on the unit circle is then $\int_{t_0}^t \mathrm{d}t/t = \log(t/t_0)$. | |
| Apr 19, 2020 at 9:10 | comment | added | Eric | But then can't the same function and integration be used to show that it's the same for a unit circle in the two dimensional case? Where's the difference? | |
| Apr 19, 2020 at 6:26 | comment | added | Timothy Budd | $\mathbb{R}_+\to S^2\subset\mathbb{R}^3: t\to x(t)$ is the position of C projected onto the unit sphere. The speed of C in $\mathbb{R}^3$ is then $v_c^2=\|x(t)\|^2+t^2\|\dot{x}(t)\|^2=2$ if $\|\dot{x}(t)\|=1/t$. | |
| Apr 19, 2020 at 2:11 | comment | added | Eric | I thought I understood your argument. But now I'm a little confused. What is $x(t)$? Can you explain a bit more in detail about "it will follow a trajectory $t\cdot x(t)$ ... (by Pythagoras)"? | |
| Apr 18, 2020 at 15:59 | comment | added | Timothy Budd | Oops, somehow I missed that comment.... let me leave the answer as a (trivial) baseline. | |
| Apr 18, 2020 at 15:54 | comment | added | Eric | Yes, that strategy is the natural one that comes to mind and was suggested by Robin in the comments. It would work if $v_c(t)=ct+k$, i.e., increasing linearly with time, for possibility 2. | |
| Apr 18, 2020 at 15:45 | history | answered | Timothy Budd | CC BY-SA 4.0 |