ISO 13541:2010 pdf free download – Space data and information transfer systems一Attitude data messages.
3.2.5.2.5 Parameters for the inertia elements of the object may be optionally given. The keyword INERTIA_REF_FRAME is provided to specify the reference frame for the inertia values, and the allowed values for this keyword are enumerated in annex A. Since the inertia matrix of a rigid body is symmetric, it is necessary to only specify six elements instead of nine. To reconstruct the full inertia matrix, the elements 121 = 112, 131 = 113, and 132 = 123. The inertia cross products used for this message assume a negative double integral.
3.2.5.2.6 Parameters for attitude change maneuvers may be optionally given for the computation of the attitude during or after maneuver execution (see reference [E4] for the simplified modeling of such maneuvers). Permissible reference frames for the torque vector (‘MAN_REF_FRAME’) shall be those allowed for the keywords ‘Q_FRAME_*, ‘EULER_FRAME_*’ or ‘SPIN_FRAME_*’, where ‘*‘ denotes ‘A’, or ‘B’, as enumerated in annex A.
3.2.5.2.7 It may become necessary to utilize particular orbit information to process Euler angle elements or a local orbit frame (e.g., LVLH, QSW) properly. An approach to this is to add a ‘COMMENT’ block specifying a particular OPM message to use in conjunction with a particular APM.
3.2.5.3 QUATERNION
3.2.5.3.1 While the range on the scalar value of the quaternion is not constrained by the specification of this standard, it is recommended that it remain non-negative (0  QC  1), which thereby constrains the rotation angle to -180 degrees 180 degrees. This avoids large attitude discontinuities of± 1 80 degrees.
3.2.5.3.2 e, e2, and e3 are the components of the rotation unit vector.
3.2.5.3.3 The message allows the occurrence of the keyword QC, and its associated value, to appear at either the beginning of the quatemion specification, or at the end (e.g., QC, QI, Q2, Q3 or Qi, Q2, Q3, QC). Quaternion rates, if specified, should follow the order of the quaternions given in the message for consistency.
3.2.5.4 EULER ANGLES
3.2.5.4.1 Valid and recommended values for the EULER_ROT_SEQ are: 123, 132, 213, 231, 312, 321. The Euler angle keywords should be given in the order specified by the EULER_ROT_SEQ (e.g., for a 321 sequence, the angular information would appear in the order Z ANGLE, Y ANGLE, X_ANGLE). Note that care must be taken in specifying the orientation of the reference frame in either the EULER_FRAME_A or EULER FRAME B with respect to each other. If necessary, this should be documented in an lCD. The order of the transformation is from left to right, where the leftmost integer represents the first rotation axis.
3.2.5.4.2 Additional, but not recommended, valid values for the EULER_ROT_SEQ are:
121, 131, 212, 232, 313, 323. These are discouraged as their use can cause confusion. To specify a repeated axis rotation in the APM, the appropriate keywords should be used to specify the axis rotation, even though keywords will be repeated (e.g., a sequence of 121 shall have the keywords X_ANGLE, YANGLE, X_ANGLE). See figure 3-6 for a full example.
3.2.5.4.3 Specification of Euler angle rotations around oniy one or two axes may be handled by entering the appropriate sequence for the desired one or two axis rotation and freely choosing the final axis of rotation and giving a value of zero for the rotation value. Therefore, this standard does not allow for a specification of less than three Euler rotation axes (e.g., for a Y then X rotation, EULER_ROT_SEQ = 212, or 213 are permissible, with a value of 0 for the final rotation; however EULER_ROT_SEQ = 21 is not). While repeated Euler rotation axes are permissible in a sequence, sequential rotations about the same axis are not.
3.2.5.4.4 Euler angle and rate ordering should be consistent with the order given in the EULER_ROT_SEQ keyword.