stealth

Hello! I'm thinking about the following problem at the moment: Four bugs sitting at the corners of the unit square begin to chase one another with constant speed, each maintaining the course in the direction of the one pursued. Describe the trajectories of their motions. What is the law of motion (in cartesian/polar coordinates)? I heard the problem is fairly known but I think I need some guidance now. Now I started with polar coordinates and got stuck with what to do with r(t) in: [math]\frac{d}{dt}\vec{r(t)}=\frac{d}{dt}{r(t)}\vec{e_r}+r(t)\frac{d}{dt}\vec{e_r}[/math] I mean the objective is a diff. equation isn't it?... but what should I do with the variable radius? Is the leangth of a side of the square of some importance? What is the implication of the fact that the course is in the direction of the other bug?

Hey guys! Nice forum! Here's my first question. How do we get this expression for the velocity: [math]\dot\vec{r}=\dot{r}+\frac{l^2}{m^2r^2}[/math], where l is the angular impulse of force I thought we could do it like this: [math]{\vec{l}}^2=l^2=(\vec{r}\times{{m\dot\vec{r}}})^2=m^2{}r^2{\dot{\vec{r}}}^2-(\vec{r}\bullet{m\dot{\vec{r}}})^2[/math] We can't simply write:[math]{\dot\vec{r}}^2={\dot{r}}^2[/math], since then l=0. But why? Which rule forbids that equality. Similarly we can't treat the scalar product above as we would wish to. So how should one proceed in this case? Thanks