Question

Write the quaternion for the following rotations in form [w,x,y,z]:

a Unit quaternion, no rotation qa =
b 180 degrees around x axis qb =
c 90 degrees around z axis qc =
d -90 degrees around z axis qd =

Answer 1

A unit quaternion represents no rotation. The quaternion for a rotation of 180 degrees around the x-axis is [-1, 0, 0, 0]. The quaternion for a rotation of 90 degrees around the z-axis is [0.707, 0, 0, 0.707].

Step-by-step explanation:

A unit quaternion represents a rotation of 0 degrees. Therefore, the quaternion for no rotation is [1, 0, 0, 0]. To find the quaternion for a rotation of 180 degrees around the x-axis, we can use the formula: qa = [cos(theta/2), sin(theta/2) * axis_x, sin(theta/2) * axis_y, sin(theta/2) * axis_z]. For a rotation of 180 degrees around the x-axis, the quaternion would be [-1, 0, 0, 0].

For a rotation of 90 degrees around the z-axis, the quaternion would be [cos(theta/2), sin(theta/2) * axis_x, sin(theta/2) * axis_y, sin(theta/2) * axis_z]. In this case, the quaternion would be [0.707, 0, 0, 0.707].