Acceleration and deceleration in best possible time-rotation

[Karwoch]

Homework Statement

I have a missile in space, and I want to rotate it by using thrusters - eight of them - two on every of four sides as force is applied pendicular - left, right, up and down - both on front and end of missile. Now I have angle to target, I know which thrusters should I turn on to rotate in right direction, and I have angular speed.

Homework Equations

How to count how much force I can apply to rotate as fast as it is possible, and not to overshot?
Second one - how to check when I need to apply opposite force to just stop exacly at target?

The Attempt at a Solution

For now I`m using "angular velocity/angle to target" value to estimate what I need. It works somewhat, but it isn`t that good as it should. I`m no physicist, or mathematican or even good computer programer, so this is very very hard for me ;) And I would love to present world a quite realistic space battles :)

 

[NascentOxygen]

Hi Karwoch. Once you start a body rotating it will continue to rotate endlessly, only ceasing if you counter that rotation by appying an opposing force for the requisite duration.

 

[Karwoch]

Exactly :) Now I have working thrusters in needed direction, I only need data when to start deceleration with full force (or 90% to have manoeuvring threshold). So, I have my angular speed, maximum angular change in delta time (or time), and angle left to target rotation. How I can "transform" my angular velocity value to angle with my maximum deceleration force?

 

[NascentOxygen]

There being no friction, if you fire a thruster with maximum thrust, the rotation can be halted by firing an opposing thruster of identical thrust for the same duration. (This assumes the loss of mass in thruster fuel causes insignificant change in the body.)

 

[Karwoch]

Yes, I do not count in loss of mass, fortunately ;) This is right, but only in case missile start accelerating from zero velocity, and when it will track something this won`t be a case. So I still need to calculate angle to angular velocity time when I should start to decelerate.

 

[NascentOxygen]

I think you are about at the point where you should draw and label a diagram, and attach it.

 

[Karwoch]

Er... I have no idea about how to do it unfortunately... And still diagram won`t give me anything if I can`t tell anything from my own knowledge... I even try to watch all lessons on angular velocities, with no much of effect. That is why I finally tried to find help here - if I would know how to do diagrams, and all physics stuff I would never bothered anyone for help... I like creating, but unfortunately I do not understand physics very well...

 

[Karwoch]

Basically, I need equation for distance (angle) traveled with constant deceleration from certain angular velocity to zero.

 

[Karwoch]

I can`t do diagrams, but I can do experiments on my environment. I had measured that angular velocity to angle is pretty constant (obviously) with 1.144 ratio. Also I measured missile acceleration in each frame, so now I just created a function which counts on this data angle which will pass with max deceleration:

        float angularVelocity = myRigidbody.angularVelocity.magnitude;

        while (angularVelocity > 0)
        {
            angle += angularVelocity * 1.1455f;
            angularVelocity -= 0.0008f;
        }

With it I`m now pretty close to what I want to achieve. But it still isn`t close enough somehow. And also, this calculate is long loop, with many missiles every frame, this will be probably not very processor efficient. If anyone would have a simpler equation, I really would appreciate it!

 

[Karwoch]

Actually this last one works! And it finally solved all my problems.