Is there any way to keep the applied torques in the old planes, even if the ship's local plane has rotated?

Question

I'm trying to make a space shooter game in Unity3D with realistic spaceship physics. I have a problem with correct rotations. When I apply torque in global coords system it will always apply them in the same global planes, even when the ship is eg. rolled to a side - if I now yaw, it will rotate it in the global system instead of yawing the ship in its local coords.

Now, when I use relative torque, I can apply yaw, then roll and it's screwed again because now the torque applied for yaw works in rotated (rolled) plane instead of the old plane.

Is there any way to keep the applied torques in the old planes, even if the ship's local plane has rotated?

Screenshots to explain the relative torque problem:

I start off with the ship aligned with the world axes. I apply relative torque to yaw.

The ship rotates in yaw plane (same as world horizontal plane).

I apply roll. The yaw is supposed to continue rotating the ship in the old plane same as world horizontal plane.

But it does not. Instead, the old yaw torque now continues in the new plane which is the local X-Z plane!

Here is the code I'm using to control the spaceship currently, using the relative torque strategy:

public class PlayerControl : MonoBehaviour
{
    private Rigidbody rb;    
    public ManeuverEngineScript FrontRightManeuverEngine;    

    void Start ()
    {
        rb = GetComponent<Rigidbody>();
    }

    void Update ()
    {
        if (Input.GetKeyDown(KeyCode.Q))
        {
            //rb.AddTorque(0f, 0f, 10f);
            rb.AddRelativeTorque(0f, 0f, 10f);
        }

        if (Input.GetKeyDown(KeyCode.W))
        {
            Debug.Log("W pressed");
            rb.AddRelativeTorque(0f, 0f, -10f);
        }

        if (Input.GetKeyDown(KeyCode.LeftArrow))
        {
            Debug.Log("LeftArrow pressed");
            //rb.AddTorque(0f, -10f, 0f);
            rb.AddRelativeTorque(0f, -10f, 0f);
        }

        if (Input.GetKeyDown(KeyCode.RightArrow))
        {
            Debug.Log("RightArrow pressed");
            rb.AddRelativeTorque(0f, 10f, 0f);
        }

        if (Input.GetKeyDown(KeyCode.DownArrow))
        {
            Debug.Log("DownArrow pressed");
            rb.AddRelativeTorque(-10f, 0f, 0f);
        }

        if (Input.GetKeyDown(KeyCode.UpArrow))
        {
            Debug.Log("UpArrow pressed");
            rb.AddRelativeTorque(10f, 0f, 0f);
        }
    }
}

Here's a "stop-motion" explanation. The first set of frames shows how I expect the rotations to happen and the second one shows how it actually takes place in Unity.

The actual:

Answer 1

First, your interpretation of what's happening in Unity is not accurate.

When you apply your roll torque, the axis of the continuing yaw drift does not shift to match the object's new local XZ plane, as we can see in this series of captures:

• The green line and ring show the object's local Y axis and local XZ plane, respectively.

• The cyan line and ring show the object's current axis and plane of rotation, respectively.

• The yellow line and ring show the object's axis and plane of rotation as they were just before the most recent torque was applied.

As we proceed from left to right, we see:

1. The object at rest, before I've applied any torques

2. After applying a yaw torque: the object yawing in its local XZ plane (green) - the cyan plane of current rotation matches this exactly.

3. After applying a roll torque: the object rotating on an inclined axis/plane (cyan) that is neither its local XZ plane (green) nor its previous plane of rotation (yellow)

And it turns out this is exactly what we expect from real physics.

After applying a torque of (0, 10, 0) for 0.02 seconds (Unity's default physics timestep), we expect to have an angular momentum of (0, 0.2, 0). Then we apply a torque of (0, 0, 10) for 0.02 seconds (assuming we waited until the forward axis was exactly parallel to the world z+ axis so we don't have to muck with coordinate systems), we expect to have an angular momentum of (0, 0.2, 0.2) - ie we should be rotating on an axis diagonal to our two torque vectors.

Although working with Euler/Tait-Bryan angles or yaw/pitch/roll terminology can get us used to the idea that rotation is separable into 3 independent components - so we might expect an object to "remember" its yaw speed and its roll speed in separate variables - in reality 3D rotation does not work that way.

An object in an inertial state (like a spaceship in a vacuum away from gravity wells and not currently firing its thrusters) has just one angular momentum vector - just one axis of rotation - and every torque we apply to it speeds/slows or moves that axis.

This change in the axis of rotation in response to torque is what's called precession. You may be used to it being a small/negligible effect for things like wheels, where the speed/torque spinning them up is much greater than the orthogonal torque deflecting them, and things like friction dampen the resulting movement. But in space with nothing to damp the motion, and with yaw thrusters exactly as strong as the roll thrusters, the combined effect is quite pronounced.

So, if your goal is realistic spaceship movement, I have good news for you: that's exactly what you're getting from this physics simulation!

But if this feels counter-intuitive as a control scheme for your game, then you'll need to come up with an alternative model. For instance, you could apply yaw and pitch using torques on the rigidbody, but apply roll using your own update script that just rotates a transform inside the body, without impacting its physics.

Answer 2

There are two methods to add torque to a rigidbody:

• AddTorque which interprets the vector in the world coordinate system
• AddRelativeTorque which interprets the vector in the local coordinate system.

You seem to want to rotate the object in the world coordinate system, so you should use AddTorque, not AddRelativeTorque.

By the way: The same applies to AddForce and AddRelativeForce.