docs(*): Add in physics formulae so I remember vaguely what I was trying to do

Game/scripts/ship.gd

@@ -28,9 +28,13 @@ func _ready():
 	gravity_scale = 1.0
 	
 	# Set custom inertia for better rotation
+	# Physics: I = m * r² (moment of inertia = mass × radius²)
+	# Lower inertia = easier to rotate, higher inertia = more stable
 	inertia = Vector3(1.0, 1.0, 1.0)
 	
 	# Create and apply low-friction physics material
+	# Physics: F_friction = μ * N (friction force = coefficient × normal force)
+	# Lower μ (friction coefficient) = less resistance to sliding
 	var ship_material = PhysicsMaterial.new()
 	ship_material.friction = 0.1  # Very low friction
 	ship_material.bounce = 0.2    # Slight bounce
@@ -73,17 +77,25 @@ func _update_camera(delta):
 
 func _update_ball_cam(delta):
 	# In ball cam, camera positions itself so the ship is between camera and ball
+	# Physics: Vector mathematics for 3D positioning
 	var ship_pos = global_transform.origin
 	var ball_pos = ball.global_transform.origin
 	
 	# Calculate direction from ball to ship
+	# Physics: Vector subtraction and normalization
+	# Direction vector: d̂ = (P₂ - P₁) / |P₂ - P₁|
 	var ball_to_ship = (ship_pos - ball_pos).normalized()
 	
 	# Position camera behind the ship relative to the ball's position
 	# This ensures the ship is always between the camera and ball
+	# Physics: Vector addition for position calculation
+	# P_camera = P_ship + d̂ * distance + height_offset
 	var camera_target_pos = ship_pos + ball_to_ship * camera_distance + Vector3.UP * camera_height
 	
 	# Smoothly move camera to target position
+	# Physics: Linear interpolation (LERP) for smooth motion
+	# P(t) = P₀ + t * (P₁ - P₀), where t ∈ [0,1]
+	# This creates exponential approach to target position
 	camera.global_transform.origin = camera.global_transform.origin.lerp(camera_target_pos, camera_smoothing * delta)
 	
 	# Make camera look at the ball
@@ -93,11 +105,17 @@ func _update_ball_cam(delta):
 		var to_ball = (ball_pos - camera_pos).normalized()
 		
 		# Create look-at transform manually
+		# Physics: 3D rotation matrices and basis vectors
+		# Uses right-hand rule: forward = -Z, up = Y, right = X
+		# Basis matrix transforms local coordinates to world coordinates
 		var camera_transform = Transform3D()
 		camera_transform.origin = camera_pos
 		camera_transform.basis = Basis.looking_at(to_ball, Vector3.UP)
 		
 		# Apply the rotation smoothly
+		# Physics: Spherical linear interpolation (SLERP) for rotation
+		# SLERP provides smooth rotation along great circle on unit sphere
+		# Maintains constant angular velocity during interpolation
 		camera.global_transform.basis = camera.global_transform.basis.slerp(camera_transform.basis, camera_smoothing * delta)
 
 func _update_ship_cam(delta):
@@ -180,10 +198,15 @@ func apply_thruster_forces(state: PhysicsDirectBodyState3D, thrust_input: Vector
 		return
 	
 	# Convert thrust input to world space forces based on ship orientation
+	# Physics: F = m * a (Newton's Second Law: Force = mass × acceleration)
+	# World force = Local force × Rotation matrix (basis transformation)
 	var ship_basis = global_transform.basis
 	var world_thrust = Vector3.ZERO
 	
 	# All thrusters should work relative to ship orientation
+	# Physics: Vector transformation from local to world coordinates
+	# F_world = R * F_local (where R is rotation matrix)
+	
 	# Forward/backward thrust (main engines)
 	world_thrust += -ship_basis.z * thrust_input.z * thrust_power
 	
@@ -199,6 +222,7 @@ func apply_thruster_forces(state: PhysicsDirectBodyState3D, thrust_input: Vector
 		world_thrust *= turbo_multiplier
 	
 	# Apply the force
+	# Physics: Δv = F * Δt / m (change in velocity = force × time / mass)
 	state.apply_central_force(world_thrust)
 
 func apply_rotation_forces(state: PhysicsDirectBodyState3D, rotation_input: Vector3):
@@ -206,19 +230,29 @@ func apply_rotation_forces(state: PhysicsDirectBodyState3D, rotation_input: Vect
 		return
 	
 	# Apply torque for rotation - simple and effective
+	# Physics: τ = I * α (torque = moment of inertia × angular acceleration)
+	# Also: α = τ / I (angular acceleration = torque / moment of inertia)
+	# Lower inertia = higher angular acceleration for same torque
 	var torque = Vector3(
-		rotation_input.x * rotation_power,  # Pitch
+		rotation_input.x * rotation_power,  # Pitch (rotation around X-axis)
-		rotation_input.y * rotation_power,  # Yaw
+		rotation_input.y * rotation_power,  # Yaw (rotation around Y-axis)
-		rotation_input.z * rotation_power   # Roll
+		rotation_input.z * rotation_power   # Roll (rotation around Z-axis)
 	)
 	
+	# Physics: Δω = τ * Δt / I (change in angular velocity = torque × time / inertia)
 	state.apply_torque(torque)
 
 func apply_drag_and_limits(state: PhysicsDirectBodyState3D, rotation_input: Vector3):
 	# Linear drag (air resistance)
+	# Physics: F_drag = -½ * ρ * v² * C_d * A (drag force equation)
+	# Simplified: v_new = v_old * drag_coefficient (exponential decay)
+	# This simulates air resistance reducing velocity over time
 	state.linear_velocity *= drag_coefficient
 	
-	# Angular drag (rotational resistance) - more aggressive when not rotating
+	# Angular drag (rotational resistance)
+	# Physics: Similar to linear drag but for rotational motion
+	# τ_drag = -C_angular * ω² (angular drag torque)
+	# Simplified: ω_new = ω_old * angular_drag (exponential decay)
 	if rotation_input.length() < 0.01:
 		# More drag when not actively rotating to stop quicker
 		state.angular_velocity *= 0.9
@@ -227,8 +261,14 @@ func apply_drag_and_limits(state: PhysicsDirectBodyState3D, rotation_input: Vect
 		state.angular_velocity *= angular_drag
 	
 	# Limit maximum speeds
+	# Physics: Terminal velocity concept - maximum achievable speed
+	# When thrust force = drag force, acceleration = 0, velocity = constant
 	if state.linear_velocity.length() > max_speed:
+		# Normalize to unit vector, then scale to max speed
+		# Physics: v̂ = v / |v| (unit vector), v_limited = v̂ * v_max
 		state.linear_velocity = state.linear_velocity.normalized() * max_speed
 	
 	if state.angular_velocity.length() > max_angular_speed:
+		# Same concept for angular velocity
+		# Physics: ω̂ = ω / |ω|, ω_limited = ω̂ * ω_max
 		state.angular_velocity = state.angular_velocity.normalized() * max_angular_speed