in a infinty 2D surface, with a cat and a mouse, the cat wants to catch the mouse. MAX speed of cat and mouse are $V_{cat} , V_{mouse}$, max acceleration are $A_{cat} , A_{mouse}$. cat and mouse both know their last $\vec V_{cat}, \vec V_{mouse}$ and make the next move at same time. catching means move to the same point.
given $V_{cat} > V_{mouse}$ , with UNLIMITED time and strategy, what are the conditions for cat to catch the mouse?
is their any results or key word of this problem?
some thoughts:
1. if cat can catch the mouse, then :
$Time_0$ : cat and mouse at same point:$(X_0,Y_0)$, with any speed and direction:$\vec V_{cat}, \vec V_{mouse}$ , (such as $\vec V_{cat} = \vec V_{mouse}$)
$Time_1$ : cat should be capable of moving to any point:$(X_1,Y_1)$ that mouse can move to.
so there should be $A_{cat} >= A_{mouse}$ ? is this necessity? is this sufficiency?
2. with unlimited time cat can guess unlimit times where mouse will move to, so it is equal to mouse move first then cat move?
3. is this relative with their staring point?