# der_quat_wrt_crv¶

Provides change of quaternion, dquat, due to elementary rotation, dcrv, expressed as a 3 components Cartesian rotation vector such that

$C(quat + dquat) = C(quat0)C(dw)$

where C are rotation matrices.

Examples

Assume 3 FoRs, G, A and B where:
• G is the initial FoR

• quat0 defines te rotation required to obtain A from G, namely: Cga=quat2rotation(quat0)

• dcrv is an inifinitesimal Cartesian rotation vector, defined in A components, which describes an infinitesimal rotation A -> B, namely:

..math :: Cab=crv2rotation(dcrv)

• The total rotation G -> B is:

Cga = Cga * Cab

• As dcrv -> 0, Cga is equal to:

$algebra.quat2rotation(quat0 + dquat),$

where dquat is the output of this function.