Hi, I need your help.

I've thought of a (relatively) simple way of getting spaceships to change directions, but I don't know Craig's equation for moving along a circle.

The variables that I use are:

x, y, z coordinates of destination

x, y, z coordinates of spaceship

x, y, z component-velocities of spaceship

My assumptions are:

speed of destination is negligible

initial speed of spaceship is greater than zero

travelling the distance d (see diagram) will not affect the angle between the spaceship and its destination

the spaceship's velocity is tangential (same direction) as its "front", so that if it sped-up, the direction would not change

the guns of the spaceship are facing 90 degrees away from the direction of its velocity (thus, guns are mounted on the side, top, or belly of the spaceship, facing away from the spaceship's centre of gravity)

the spaceships engines are at the spaceship's centre of gravity

torque can be altered instantaneously (can be changed later)

no acceleration due to gravity

the distance between the spaceship and destination is much, much greater than ((360 degrees / maximum turn rate in degrees per second) * speed of spaceship in units per second) / 2(pie)

rem change in angle required = angle between spaceship's direction and direction of destination, + 90 degrees (because spaceship is pointed towards the centre of the arc that it turned in)

My most important assumption:

Either:

1)the direction of the spaceship's velocity is perpendicular to the direction of the destination

or

2)there is a way to derive a spherical trajectory using a 2D circle trajectory plus a required change in the z-axis (if assumption 1 is false)

My end-product is:

The spaceship rotates for one second so that it is now moving sideways through space

The spaceship is pointed towards the centre of a circle, where 2(pie)*radius = perimeter = (360 degrees / maximum turn rate in degrees per second) * speed of spaceship in units per second

The spaceship turns for time = change in angle required / maximum turn rate in degrees per second

The spaceship is still pointed towards the centre of the circle, and its top, side, or belly is facing the destination.

The spaceship is moving towards the destination, but not really

for example, if the spaceship is travelling in the direction of +x, and the destination requires it travel in the directions -x, -y, -z, then:

1) the spaceship can turn in a circle, correcting its direction of movement to -x, -y

2) the spaceship can turn in a circle, correcting its direction of movement to +x, -y, -z

3) the spaceship can turn in a spherical trajectory (see important assumptions 1 and 2)

4) the spaceship can undergo two maneouvres!!! The first arc will correct x and y vectors, and the second arc will be a circle tangent to the z-axis

Number 3 is too hard for me to program, since I've never learned spherical vectors.

Number 4 will make the spaceship look it is doing the loop-de-loop (silly).

Rem Speed remains constant throughout the entire process.

I have some trigonometry (angles) and time variables mapped out in my head (spaceship turns during the second before it begins its arc).

Unfortunately, I don't know Craig's equations for the displacement of a spaceship when given a circular trajectory (with radius and acceleration and location of circle's centre given).

**Help!**

Here is a diagram of what I have so far:

The spaceship is in blue, pointing in the direction of the vertice of the blue arrow.

remember that because the destination is so far away, θ1 = θ2

green line is the distance the spaceship travels while turning (and NOT accelerating)

in total, the spaceship travels 270 degrees - θ1 (270 degrees is an arbitrary value based on the spaceships initial direction)

note: if the guns were on the left-hand side of the spaceship, then the spaceship would turn in a circle to the right 180 degrees - θ1

once the required turn is complete, the spaceship stops accelerating, and is travelling towards its destination (if θ1 = θ2).

circle radius (red) = ((360 degrees / maximum turn rate in degrees per second) * speed of spaceship in units per second) / 2(pie)

Remember that this only accounts for x and y directions (or x and z, or y and z).

I cannot due spherical coordinates, so I need help!

I like this method of movement because when the spaceship wants to dodge a projectile fired from the destination (say it is targetting a ship) then the spaceship is in the optimal direction to thrust forwards and dodge this shot (like in the game Asteroids, you have to turn away from an asteroid before dodging).

That was a heck of a post, and I didn't even start any trigonometry.

I'm starting to see that Fragmented Galaxy is a large-scale project.