# Movement along a curve

1. Nov 8, 2008

### Sketchys

This is my first post here, and I'm not really sure where I should have made it. If it's in the wrong place, please go easy on me and could an admin move it to where it should be.

It's not strictly a homework problem, but it's fairly specific question, and not very deep or philosophical.

I have a moving object. It has an initial location (x,y), heading and speed.

I also have a destination point (x,y).

What I would like, is some way to calculate the constant acceleration and turning (ie. degrees per second) required to get the object to the destination point. I am not particularly interested in the final speed or heading.

I realize it's a pretty big ask, but if anyone could help me, or perhaps point me in the direction of some relevant articles or even other forums, then I'd really appreciate it.

Thanks :)

2. Nov 8, 2008

### CEL

If there is no constraints, you can consider your movement to be circular uniform. So, your starting and destination points belong to a circle and the initial velocity is tangent to the circle at the starting point.
Knowing two points and a tangent, you can calculate the radius R of the circle. The centripetal acceleration is $$V^2/R$$

3. Nov 8, 2008

### Sketchys

Hmmm. Good point.

There will be constraints on the maximum speed and turning rate.

I had intended to calculate the required values first, and then check if they fall within the limits after, but I see that won't work.

I guess in reality, I'm looking for the the minimum amount of turning required, and the corresponding acceleration.

4. Nov 8, 2008

### CEL

With constraints you will probably need to use Lagrange multipliers.

5. Nov 9, 2008

### Sketchys

Well that's just *far* too complicated for me to be able to understand inside of the next year, so I guess I'll have to manage without :(