Learning Lua by building Asteroids. This function moves the spaceship given thrust input.

Acceleration Vectors

playerShip = {
    position = {
        x = 100,
        y = 60
    },
    rotation = 0,
    velocity = {
        speed = 12.0, 
        direction = 0
    },
    points = {
        { x =  8, y =  0 },
        { x = -8, y =  6 },
        { x = -4, y =  0 },
        { x = -8, y = -6 },
        { x =  8, y =  0 }
    },
    accelerationConst = 1.0,
    rotationConst = 0.1
}

-- See "Basic Vector Operations," http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html
function acceleratePlayerShip()
    -- Adds the current vector `a` of the ship to the new vector `b` of the ship to 
    -- give a resulting `r` vector and theta (angle)

    -- get the original magnitude (speed) and rotation vector
    magnitudeA = playerShip.velocity.speed
    directionA = playerShip.velocity.direction
    ax = magnitudeA * math.cos(directionA)
    ay = magnitudeA * math.sin(directionA)

    -- get the new vector based on an increment of `accelerationConst` on the velocity and 
    -- the rotation of the ship
    magnitudeB = playerShip.velocity.speed + playerShip.accelerationConst
    directionB = playerShip.rotation
    bx = magnitudeB * math.cos(directionB)
    by = magnitudeB * math.sin(directionB)

    -- combine the vectors to form a right triangle. the hypotenuse is the new magnitude
    rx = ax + bx
    ry = ay + by
    R = math.sqrt(math.pow(rx,2) + math.pow(ry,2))    
    theta = math.atan(ry/rx)

    playerShip.velocity.speed = R
    playerShip.velocity.direction = theta
end

acceleratePlayerShip()