Your question makes sense. Calculating the orientation acceleration of a solid perfect sphere using quaternions is indeed a suitable approach. Quaternions provide a convenient way to represent and manipulate orientations in three-dimensional space.
To calculate the orientation acceleration, you can follow these steps:
1. Represent the initial orientation of the sphere using a quaternion. Let's call it `q0`, where `q0 = [w0, x0, y0, z0]`. The quaternion represents the rotation from the reference orientation (e.g., identity quaternion) to the initial orientation.
2. Calculate the angular velocity of the sphere using the known forces and torques acting on it. Let's call it `omega = [p, q, r]`, where `p` represents the roll rate, `q` represents the pitch rate, and `r` represents the yaw rate.
3. Convert the angular velocity `omega` to a quaternion derivative `dq/dt` using the formula:
dq/dt=0.5*q*[0,p,q,r]
Here, `q` is the quaternion representing the current orientation of the sphere.
4. Integrate the quaternion derivative `dq/dt` over time to obtain the new quaternion `q` representing the updated orientation. You can use your non-stiff differential equation solver "gni_vstrvl2" to calculate the quaternion acceleration `dq/dt` and update the quaternion `q` accordingly.
By following these steps, you should be able to calculate the orientation acceleration of the sphere using quaternions and update the roll, pitch, and yaw angles accordingly.
Note: When using quaternions, it's important to normalize them after each integration step to ensure they remain unit quaternions (i.e., their magnitude is 1).
