Slowly dissecting the problem there and your response is helping, it's made me think how to structure it properly.

I need to rotate, then translate my object along Y, then draw it along the path.

I'll tinker later and let you know - cheers

when i've done this in the past i've just used the usual position, velocity and acceleration vectors.

on every loop
position = position + velocity;
velocity = (drag * velocity) + acceleration;

only the acceleration vector depends on rotation and is 0 if no button is pressed.

the 'easing' is done by the drag co-efficient (usually something like .99, although 1.0 is more realistic space behaviour)

drawing the ship rotated at the correct position is the usual 'rotate around centre' issue, probably covered by allonestring up there.

1. player_ship pShip;
2. void setup()
   {
   size(600, 600);
   background(165);
   frameRate(30);
   pShip = new player_ship();
   }
4. void draw()
   {
   pShip.ship_draw();
   }
6. void keypressed()
   {
   pShip.ship_thrust();
   }
8. class PVector
   {
   float x;
   float y;
   
   PVector(float my_x, float my_y)
   {
   my_x = x;
   my_y = y;
   }
   
   void add(PVector v)
   {
   x = x + v.x;
   y = y + v.y;
   }
   }
10. class player_ship
    {
    PVector player_location;
    PVector player_speed;
    float player_thrust;
    
    player_ship()
    {
    player_location = new PVector(0, 0);
    player_speed = new PVector(0, player_thrust);
    }
    
    void ship_draw()
    {
    ship_thrust();
    translate(width/2, height/2);
    pushMatrix();
    translate(player_location.x, player_location.y);
    pushMatrix();
    translate(0, 10);
    rotate(0);
    popMatrix();
    triangle(-10, 10, 0, -20, 10, 10);
    popMatrix();
    }
    
    void ship_thrust()
    {
    if (key == 'w')
    {
    player_location.add(player_speed);
    player_thrust = -10;
    println(player_speed.y);
    }
    }
11. }

I know by the fact it's not doing anything I've either got it COMPLETELY wrong or it's something simple

1) Never call framerate().

1. class player_ship
   {
     PVector player_location;
     PVector player_speed;
     float player_thrust, rotation;
    
     player_ship()
     {
       player_location = new PVector(0, 0);
       player_speed = new PVector(0, player_thrust);
     }
    
     void ship_draw()
     {
       ship_thrust()
       translate(width/2, height/2);
       pushMatrix();
       translate(player_location.x, player_location.y);
       pushMatrix();
       translate(0, 10);
2.     rotate(rotation);
       translate(0, -10);
       triangle(-10, 10, 0, -20, 10, 10);
       popMatrix();
       popMatrix();
     }
    
     void ship_thrust()
     {
       player_thrust = constrain(player_thrust, 0, 10);
       player_location.y = player_location.y + player_speed.y;
       println(+player_thrust);
       if (keyPressed && key == 'w')
       {
         player_thrust = -1;
         player_speed.y = player_speed.y + (player_thrust * 1.3);
       }
       if (keyPressed && key == 'd')
       {
         rotation = rotation + PI/20;
       }
     }
   }

my version.

up = thrust, left and right to rotate.

1. // acd 20110809
   
2. 
   
3. Ship ship;
4. 
   
5. void setup() {
6.   size(600, 600);
7.   background(165);
8.   ship = new Ship();
9. }
10. 
    
11. void draw() {
12.   background(0);
13.   ship.move();
14.   ship.draw();
15. }
16. 
    
17. void keyPressed() {
18.   switch (keyCode) {
19.     case UP:
20.       ship.thrust();
21.       break;
22.     case LEFT:
23.       ship.rotateLeft();
24.       break;
25.     case RIGHT:
26.       ship.rotateRight();
27.       break;
28.   }
29. }
30. 
    
31. void keyReleased() {
32.   ship.noThrust();
33. }
34. 
    
35. public static final float INCR = .1;      // spin speed
    
36. public static final float ACC = .2;      // accleration
37. 
    
38. class Ship {
39.   PVector location;
40.   PVector velocity;
41.   PVector acceleration;
42.   float angle = 0;
43. 
    
44.   Ship() {
45.     location = new PVector(0, 0);
46.     velocity= new PVector(0, 0);
47.     acceleration = new PVector(0, 0);
48.   }
49.  
50.   void move() {
51.     location.add(velocity);
52.     velocity.mult(.995);          // drag
53.     velocity.add(acceleration);  // add acceleration
54.    
55.     // wraparound
56.     if (location.x < -width / 2) {
57.       location.x = width / 2;
58.     } else if (location.x > width / 2) {
59.       location.x = -width / 2;
60.     }
61.     if (location.y < -height / 2) {
62.       location.y = height / 2;
63.     } else if (location.y > height / 2) {
64.       location.y = -height / 2;
65.     }
66.   }
67. 
    
68.   void draw() {
69.     stroke(255);
70.     noFill();
71.     pushMatrix();
72. // centre screen
    
73.     translate(width / 2, height / 2);
74. // position
    
75.     translate(location.x, location.y);
76. // orientation
    
77.     rotate(angle + HALF_PI);
78.     triangle(-10, 10, 0, -20, 10, 10);
79.     popMatrix();
80.   }
81.  
82.   void thrust() {
83.     // force is applied at an angle
84.     acceleration = new PVector(ACC * cos(angle), ACC * sin(angle), 0);
85.   }
86. 
    
87.   void noThrust() {
88.     acceleration = new PVector(0, 0, 0);
89.   }
90.  
91.   void rotateLeft() {
92.     angle -= INCR;
93.   }
94. 
    
95.   void rotateRight() {
96.     angle += INCR;
97.   }
98. }

the trick, if trigonometry is a trick, is that the acceleration is applied at an angle.

Wow that has REALLY cleared things up for me now I've seen an example. I'll dissect this so I'm sure I fully inderstand it thankis so much.