feat(gamecli): implement pure Physics.Step with unit tests

GameCli/Physics.cs

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+namespace GameCli;
+
+/// <summary>
+/// Pure physics stepper. All constants are public so training/tuning can inspect them.
+/// Explicit Euler integration at fixed dt.
+/// </summary>
+public static class Physics
+{
+    public const float Dt = 0.02f;                 // 50 Hz
+    public const float Gravity = 0.5f;             // world units / s^2, +Y (downward)
+    public const float MainThrust = 1.2f;          // world units / s^2 along body-up
+    public const float SideTorque = 4.0f;          // rad / s^2
+    public const float SideLateralImpulse = 0.15f; // world units / s^2 along body-x
+    public const float LinearDrag = 0.10f;         // per-second
+    public const float AngularDrag = 0.50f;        // per-second
+
+    public const int ActionNoop = 0;
+    public const int ActionLeft = 1;
+    public const int ActionMain = 2;
+    public const int ActionRight = 3;
+
+    /// <summary>
+    /// Advance the ship state by one dt given a discrete action.
+    /// Gravity is always applied. Thrusters add to acceleration/torque.
+    /// </summary>
+    public static ShipState Step(ShipState s, int action)
+    {
+        // Start with gravity.
+        float ax = 0f;
+        float ay = Gravity;
+        float torque = 0f;
+
+        // Body-up direction in world coords, given angle:
+        //   angle=0    → (0, -1)    "up" on screen (Y is down)
+        //   angle=+π/2 → (+1,  0)   right
+        //   angle=+π   → (0, +1)    down
+        float sinA = MathF.Sin(s.Angle);
+        float cosA = MathF.Cos(s.Angle);
+        float bodyUpX = sinA;
+        float bodyUpY = -cosA;
+        // Body-right direction (perpendicular, rotated +90°):
+        float bodyRightX = cosA;
+        float bodyRightY = sinA;
+
+        switch (action)
+        {
+            case ActionMain:
+                ax += bodyUpX * MainThrust;
+                ay += bodyUpY * MainThrust;
+                break;
+            case ActionLeft:
+                torque -= SideTorque;
+                ax += bodyRightX * SideLateralImpulse;
+                ay += bodyRightY * SideLateralImpulse;
+                break;
+            case ActionRight:
+                torque += SideTorque;
+                ax -= bodyRightX * SideLateralImpulse;
+                ay -= bodyRightY * SideLateralImpulse;
+                break;
+            case ActionNoop:
+            default:
+                break;
+        }
+
+        // Integrate velocity, apply linear drag, integrate position.
+        float vx = (s.VX + ax * Dt) * (1f - LinearDrag * Dt);
+        float vy = (s.VY + ay * Dt) * (1f - LinearDrag * Dt);
+        float x = s.X + vx * Dt;
+        float y = s.Y + vy * Dt;
+
+        // Angular: same pattern.
+        float w = (s.AngularVelocity + torque * Dt) * (1f - AngularDrag * Dt);
+        float angle = s.Angle + w * Dt;
+
+        return new ShipState(x, y, vx, vy, angle, w);
+    }
+}