North Pole 3 Relationship between the third Euler

North Pole 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 Initial attitude: ZYZ Euler angles (0, 0, 0) Satellite Z-axis points North pole Satellite X-axis points Spring equinox DEC Z X Z Y Spring Equinox RA 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

X-ray telescope is like a pin-hole camera, such that the “mirror image” is projected on the detector plane. North Pole 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 Detector plane DETY DEC North DETX DEC X-ray telesope Z DETX Y 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. Spring Equinox RA X DETY East RA Euler angle : (0, 90, 0) Relationship of sky coordinate and detector coordinate ZYZ Euler angles (0, 90, 0) Satellite Z-axis points Spring equinox Satellite X-axis points South pole

North Pole 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 ZYZ Euler angles (0, 90, 0) Satellite Z-axis points Spring equinox Satellite X-axis points South pole Rotate y around Z axis ZYZ Euler angles (0, 90, y) Detector Plane DETY DEC North DETX y DEC DETY Spring Equinox RA DETYRoll-angle DETY y East RA angle: (0, 90, y) Euler angle: (0, 90, 0) Z y y DETXY X Normally, “roll-angle” is defined as the angle from North to DETY axis measured in counter-clockwise Now, we see that Roll-angle=90 -y