Ship Controls modeling Real life Physics

Question

I am working on a 2D ship that will fly around in space (for now, no friction or gravity). The controls are similar to the game Asteroids. My problem is that I am having trouble connecting some variables to real life applications.

For example, if I'm defining the ships velocity, which in real physics is V=distance traveled (or change in position)/time. Should velocity be a Vector2 or just a float (or int). It's how far an object moves so I would think it to be just a single integer or number but then again, your moving on an X and Y axis so shouldn't there be two velocities? One for the X and another for the Y? The velocity being a vector2 actually works really well but when I'm doing other formulas, which are floats or ints, that require velocity I run into issues because I don't have a single number then.

Another issue i'm having trouble grasping is the direction. My code for the direction is:

shipVariables.shipDirection = new Vector2((float)Math.Sin(shipVariables.shipRotation), -(float)Math.Cos(shipVariables.shipRotation));

Which works but it will immediately turns the ship if you rotate the object while moving "forward". My most successful approach to this method was doing this:

shipVariables.shipDirection += new Vector2((float)Math.Sin(shipVariables.shipRotation), -(float)Math.Cos(shipVariables.shipRotation));

The effect I like is that instead of just turning, it essentially has to overcome the previous direction to move to the next. The part I don't like is that it gains speed way to much and it's supposed to just be a direction, not a direction and magnitude.

If I have the velocity and I can get the direction, I will be able to calculate everything else with other formulas that I know (momentum, acceleration, etc...).

Any tips to lead me in the right directions would be great, thanks.

Answer 1

Physics for simple points in 2D is basically the same as doing 1D physics twice - once for each dimension (X and Y). So you can use the same formulas you would use on floats on Vector2s and it generally "just works".

But if you add rotation, you must calculate a 1D angular "dimension" as well. (It's more of a "degree of freedom".)

So start with your variables:

float angle;
// You could have a "float angularVelocity" here if you wanted
Vector2 position;
Vector2 velocity;

And then update something like this:

if(leftKey)
    angle -= rotateAmount;
if(rightKey)
    angle += rotateAmount;

// Note: A proper cartesian coordinate system with "Y+ = up" would be (cos, sin).
//       But I'll just use what you have:
Vector2 direction = new Vector2((float)Math.Sin(angle), -(float)Math.Cos(angle));

float thrust = thrustKey ? 1f : 0f;

velocity += direction * thrust * time;
position += velocity * time;

Finally: Generally don't use int for physics. It is for integer (whole) values, which makes it difficult to get the desired results. A Vector2 is made up of two floats.