I am working on a problem and I need to convert radius of rotation to angles of rotation. So there is a point moving on a line in R^2. The point will change trajectory by turning. There is a constraint to the turning. The point has a minimal radius of rotation to respect (let's call it r). I would like to obtain the maximum angle between the original trajectory and the new path. Of course I could choose a arbitrary close point on the circle and compute a slope and then the angle.
So for example. let the point be at P(-1,0) for t=0. It will start turning from that point (r=1). It was moving on the line x=-1 to the positives. It will "turn right" bounded by the circle (x-1)^2+y^2=^2. I don't see how calculus may help. The point was already running on the tangent line of the circle. So my idea was to choose a point on the circle and compute a slope. But later I will need to compare different angles with different speed. So the choosing can't be that arbitrary since I'll use the same every time. If I choose the point in function of the speed I may (or not) introduce a bias.
Do you know what people usually do to convert radius to angle? The angle is a simplification. Like a running football player can turn close to 90 degrees but a truck can't maybe the truck can turn at 15 degrees top. The football player has a smaller radius of rotation than the truck.
I could compute the angle one unit of time later (dependent of speed). I could normalize the speed first by computing the angle at a small distance (constant).
Please give your opinion
So for example. let the point be at P(-1,0) for t=0. It will start turning from that point (r=1). It was moving on the line x=-1 to the positives. It will "turn right" bounded by the circle (x-1)^2+y^2=^2. I don't see how calculus may help. The point was already running on the tangent line of the circle. So my idea was to choose a point on the circle and compute a slope. But later I will need to compare different angles with different speed. So the choosing can't be that arbitrary since I'll use the same every time. If I choose the point in function of the speed I may (or not) introduce a bias.
Do you know what people usually do to convert radius to angle? The angle is a simplification. Like a running football player can turn close to 90 degrees but a truck can't maybe the truck can turn at 15 degrees top. The football player has a smaller radius of rotation than the truck.
I could compute the angle one unit of time later (dependent of speed). I could normalize the speed first by computing the angle at a small distance (constant).
Please give your opinion
