I am using Bullet Physic library to program some function, where I have difference between orientation from gyroscope given in quaternion and orientation of my object, and time between each frame in milisecond. All I want is set the orientation from my gyroscope to orientation of my object in 3D space. But all I can do is set angular velocity to my object. I have orientation difference and time, and from that I calculate vector of angular velocity [Wx,Wy,Wz] from that formula: W(t) = 2 * dq(t)/dt * conj(q(t))

My code is:

btQuaternion diffQuater = gyroQuater - boxQuater;
btQuaternion conjBoxQuater = gyroQuater.inverse();
btQuaternion velQuater = ((diffQuater * 2.0f) / d_time) * conjBoxQuater;

And everything works well, till I get:

1> rotating around Y axis, angle about 60 degrees, then I have these values in 2 critical frames:

x: -0.013220    y: -0.038050    z: -0.021979    w: -0.074250    - diffQuater
x: 0.120094    y: 0.818967    z: 0.156797    w: -0.538782    - gyroQuater
x: 0.133313    y: 0.857016    z: 0.178776    w: -0.464531    - boxQuater
x: 0.207781    y: 0.290452    z: 0.245594    - diffQuater -> euler angles
x: 3.153619    y: -66.947929    z: 175.936615    - gyroQuater -> euler angles
x: 4.290697    y: -57.553043    z: 173.320053    - boxQuater -> euler angles
x: 0.138128    y: 2.823307    z: 1.025552    w: 0.131360    - velQuater
d_time: 0.058000

x: 0.211020    y: 1.595124    z: 0.303650    w: -1.143846    - diffQuater
x: 0.089518    y: 0.771939    z: 0.144527    w: -0.612543    - gyroQuater
x: -0.121502    y: -0.823185    z: -0.159123    w: 0.531303    - boxQuater
x: nan    y: nan    z: nan               - diffQuater -> euler angles
x: 2.985240    y: -76.304405    z: -170.555054    - gyroQuater -> euler angles
x: 3.269681    y: -65.977966    z: 175.639420    - boxQuater -> euler angles
x: -0.730262    y: -2.882153    z: -1.294721    w: 63.325996    - velQuater
d_time: 0.063000

2> rotating around X axis, angle about 120 degrees, then I have these values in 2 critical frames:

x: -0.013045    y: -0.004186    z: -0.005667    w: -0.022482    - diffQuater
x: -0.848030    y: -0.187985    z: 0.114400    w: 0.482099    - gyroQuater
x: -0.834985    y: -0.183799    z: 0.120067    w: 0.504580    - boxQuater
x: 0.036336    y: 0.002312    z: 0.020859    - diffQuater -> euler angles
x: -113.129463    y: 0.731925    z: 25.415056    - gyroQuater -> euler angles
x: -110.232368    y: 0.860897    z: 25.350458    - boxQuater -> euler angles
x: -0.865820    y: -0.456086    z: 0.034084    w: 0.013184    - velQuater
d_time: 0.055000

x: -1.721662    y: -0.387898    z: 0.229844    w: 0.910235    - diffQuater
x: -0.874310    y: -0.200132    z: 0.115142    w: 0.426933    - gyroQuater
x: 0.847352    y: 0.187766    z: -0.114703    w: -0.483302    - boxQuater
x: -144.402298    y: 4.891629    z: 71.309158    - diffQuater -> euler angles
x: -119.515343    y: 1.745076    z: 26.646086    - gyroQuater -> euler angles
x: -112.974533    y: 0.738675    z: 25.411509    - boxQuater -> euler angles
x: 2.086195    y: 0.676526    z: -0.424351    w: 70.104248    - velQuater
d_time: 0.057000

2> rotating around Z axis, angle about 120 degrees, then I have these values in 2 critical frames:

x: -0.000736    y: 0.002812    z: -0.004692    w: -0.008181    - diffQuater
x: -0.003829    y: 0.012045    z: -0.868035    w: 0.496343    - gyroQuater
x: -0.003093    y: 0.009232    z: -0.863343    w: 0.504524    - boxQuater
x: -0.000822    y: -0.003032    z: 0.004162    - diffQuater -> euler angles
x: -1.415189    y: 0.304210    z: -120.481873    - gyroQuater -> euler angles
x: -1.091881    y: 0.227784    z: -119.399445    - boxQuater -> euler angles
x: 0.159042    y: 0.169228    z: -0.754599    w: 0.003900    - velQuater
d_time: 0.025000

x: -0.007598    y: 0.024074    z: -1.749412    w: 0.968588    - diffQuater
x: -0.003769    y: 0.012030    z: -0.881377    w: 0.472245    - gyroQuater
x: 0.003829    y: -0.012045    z: 0.868035    w: -0.496343    - boxQuater
x: -5.645197    y: 1.148993    z: -146.507187    - diffQuater -> euler angles
x: -1.418294    y: 0.270319    z: -123.638245    - gyroQuater -> euler angles
x: -1.415183    y: 0.304208    z: -120.481873    - boxQuater -> euler angles
x: 0.017498    y: -0.013332    z: 2.040073    w: 148.120056    - velQuater
d_time: 0.027000

The problem is the most visible in diffQuater -> euler angles vector. Can someone tell me why it is like that? and how to solve that problem?

All suggestions are welcome.