Relationship between the third Euler angle and the roll angle 第3オイラー角とロール角の関係 Relationship between the third Euler angle and the roll angle North Pole Initial attitude:ZYZ Euler angles (0,0,0) Satellite Z-axis points North pole Satellite X-axis points Spring equinox RA DEC Spring Equinox Z Z X Y X No rotation around Z 90 deg around Y ZYZ Euler angles (0,90,0) Satellite Z-axis points Spring equinox Satellite X-axis points South pole

Relationship between the third Euler angle and the roll angle X-ray telescope is like a pin-hole camera, such that the “mirror image” is projected on the detector plane. In order to reproduce the correct sky image, it is necessary to see the image from behind, or “flip” the image. Usually, we define the detector X- and Y-axis (DETX, DETY), such that DETX=SATX　 DETY=-SATY. 第3オイラー角とロール角の関係 Relationship between the third Euler angle and the roll angle North Pole RA DEC Spring Equinox RA DEC Detector plane DETX DETY X-ray telesope Z Y DEC RA Relationship of sky coordinate and detector coordinate Euler angle :(0,90,0) North DETY DETX X East ZYZ Euler angles (0,90,0) Satellite Z-axis points Spring equinox Satellite X-axis points South pole

Relationship between the third Euler angle and the roll angle 第3オイラー角とロール角の関係 Relationship between the third Euler angle and the roll angle North Pole ZYZ Euler angles (0,90,0) Satellite Z-axis points Spring equinox Satellite X-axis points South pole RA DEC Spring Equinox RA DEC Rotate y around Z axis ZYZ Euler angles (0,90,y) Detector Plane DETY DETY y Z Y North DETX DETY DETX DETX DETY DETX DEC y X Normally, “roll-angle” is defined as the angle from North to DETY axis measured in counter-clockwise Roll-angle East RA Euler angle:(0,90,0) Euler angle:(0,90, y) Now, we see that Roll-angle=90-y