Question
Aircrafts are simulated as these objects, the orientations of which can be described by the Tait–Bryan angles, corresponding to yaw, pitch, and roll. For 10 points each:
[10m] Name these objects whose orientations are more commonly represented by the Euler angles. These non-deformable objects have constant distance between any two points.
ANSWER: rigid bodies [or rigid objects]
[10e] The Euler equations describe the amount of this quantity applied to a rotating rigid body. This quantity is equal to the moment of inertia times angular acceleration, as defined by a rotational analogue of Newton’s second law.
ANSWER: torque [accept applied torque]
[10h] Instead of Euler angles, computations for rigid body rotation may use the Cayley–Klein parameters, which form elements of this group. The unit quaternions are representations of this group, which has a double cover of SO(3) (“S-O-three”).
ANSWER: SU(2) (“S-U-two”) [or SU(2, C) or special unitary group of degree 2 (over the complex numbers); prompt on SU(n) or special unitary group; reject “special linear group” or “SL(2)” or “unitary group” or “U(2)”]
<Physics>