Revision #2491 → #2741 · back to history
addedEuler angles74c6bb7dbac3
addedEuler angles for frames3d8c8d0880c9
addedClassic vertical zero conventionfeaccd57f63d
addedAlternative horizontal zero convention1bf23a93a2b3
addedDefinitions by geometry or rotationseb48a6c18796
addedThree rotations sufficeb195597cdd34
addedExtrinsic rotations62dbb2074353
addedIntrinsic rotations2fd57a5ee58d
addedPrimed axis notationf2cc1f3d5915
addedEuler angle symbols58b67c7e5359
addedTwelve rotation-axis sequences407c0048eb5c
addedProper Euler angles28019cccfcec
addedTait-Bryan angles14d53c300633
addedTait-Bryan aliases255ec4c3c5da
addedBroad Euler angle terminologyce6c69f0647d
addedClassic Euler angles8b23c61be5b4
addedLine of nodes9825a6c01289
addedLine of nodes as common perpendicular78952738be72
addedGeometric Euler anglesab9040b441a2
addedFirst geometric Euler angle24ebd3e60ef4
addedSecond geometric Euler angle4ef852fbb114
addedThird geometric Euler angle32aa6f76a6af
addedSame-handed frames condition2f5aae49503a
addedIntrinsic rotations7b53a5564374
addedIntrinsic axes change orientation0529ec25c349
addedIntrinsic rotations reach any orientationaf3cfc9d2cbd
addedEuler angles by intrinsic rotations03edfee70ca3
addedSuccessive frame orientations43c90b15c5d6
addedIntrinsic line of nodes1d6c1704cbc0
addedNode as primed x-axis60ba965a6131
addedThird rotation preserves Z orientationc3c09cda0e15
addedFinal Z equals double-primed za8e0ae60f606
addedFirst intrinsic Euler rotation6966207b4592
addedSecond intrinsic Euler rotation92ad4b2be16a
addedThird intrinsic Euler rotation96fcbe6318ea
addedWigner ZX'Z' convention8a664acc952f
addedHirschfelder ZY'Z' convention8f5da6d7e452
addedExtrinsic rotationsaec43afcc880
addedExtrinsic fixed frame9921f4d92279
addedExtrinsic rotations reach any orientationfa9685252212
addedEuler angles as rotation amplitudesb65323b0c171
addedExtrinsic z rotation stepcb5bce75a7a7
addedExtrinsic x rotation stepeb95a21616e9
addedFinal extrinsic z rotation step7c4c348a74fd
addedZXZ sequence notationd589d340757b
addedFixed-axis convention examplesfe185f7496b6
addedIntrinsic rotation from rotating frame actiond64338f76f99
addedIntrinsic 3-1-3 notation36b095a9c3da
addedRight-hand angle convention4c627b9c8877
addedPositive angle signf64a585db5c4
addedNegative angle signb472c2d892d7
addedAlpha and gamma range0d986e4f6d84
addedAlpha and gamma valid range4c81217fd071
addedBeta rangefb90fc489735
addedBeta valid rangesed316ee3e2d1
addedEuler angle uniqueness except singular case3f7e7f7fe55e
addedAligned z axes ambiguity3c6823389d3a
addedOpposite z axes ambiguity329f40faa5d2
addedGimbal lock ambiguity1320f7972dc6
addedProper Euler axis choices3072251ef74b
addedProper Euler repeated axis64d4ca631c7e
addedProper Euler sequence list49d171cecdbd
addedPrecession, nutation, and intrinsic rotation6c32ebf4ff76
addedMixed axes of rotation system432575f05684
addedPrecession motiona188d2aee8ec
addedNutation motion6b4e4697c8cf
addedIntrinsic rotation motion8f3f37dd6895
addedOrientation-change decomposition depends on framed41a807d6170
addedTop intrinsic rotationf6e71f73e6f5
addedTop precession87a7cde002ec
addedTop nutation566a120143e2
addedPrecession matrix independence21e531d21885
addedMovements as gimbal setc31f6c8f2738
addedIntermediate frames901255bcf8c4
addedGimbal rings reach any orientation8cf1efa7c3d4
addedTait-Bryan angles74d7a1ac1bba
addedAerospace horizontal attitude convention4f81bdf70ff4
addedAircraft world-frame orientationdddb2772e488
addedVehicle axis convention variabilityfb0f7240af99
addedTait-Bryan distinct axese67d2094ace4
addedProper Euler repeated first-third axis712e025c82ac
addedProper Euler line of nodes planesab60eda05233
addedTait-Bryan line of nodesb0dc64db828c
addedTait-Bryan extrinsic rotations12c08035ddd2
addedTait-Bryan intrinsic rotationsfa7691aa49b7
addedTait-Bryan axis choicesca3ecf14ca92
addedYaw, pitch, and roll conventionbb29606ae00e
addedTait-Bryan sign conventions95a9386807c8
addedPsi and phi rangeb54773082439
addedTheta range0d405c55635c
addedHeading, bank, and elevation framesfc6233082427
addedMiddle-frame elevationb0dac7ac79ed
addedAircraft principal-axis rotationsc5c9956b5470
addedYaw gives bearing5be4e8a484b6
addedPitch gives elevation4ca6769de507
addedRoll gives bank angleb86b0ff5bafb
addedYaw, pitch, and roll name18d5aa25d6e0
addedYaw-pitch-roll order dependenceb9837bbcdceb
addedNautical angles14acfe7779e3
addedCardan angles1d8d2bcde017
addedFinding Euler angles of a framef7a6b19636d4
addedMatrix column methodf3bb7157ac11
addedElemental geometry method4276ee7f1350
addedZXZ and ZYX conventions4c5af4e7a1a7
addedOther conventions by axis renaming0249af0f2611
addedProper Euler frame-coordinate formulase1bbf81d9561
addedProper Euler double projectionb563507ae946
addedProper Euler analogous construction7c97c8ef45d7
addedProper Euler inverse cosine formulasfd07ec133263
addedTait-Bryan frame-coordinate formulas3e306b731c7b
addedNegative theta convention06ca5d6951d9
addedTait-Bryan analogous formulasa18e6aebb7ab
addedTait-Bryan expression formulasf03c30f7a2a8
addedInverse trigonometric ambiguity669dac19d18e
addedGeometric solution uniquenessa6f95742eee0
addedRotation-sequence multiple solutions8bbff109d958
addedAngle-range unique solutionc014d39faaa8
addedNonunique sequence without ranges99f56c97d8aa
addedAtan2 angle representationb5116d4564e4
addedEuler angles as orientation representationa76f60d5f297
addedChange between orientation conventions81ffbbbcfc33
addedThree parameters for 3D orientationa3b0229dbc66
addedCommon orientation representationsd5108f470f28
addedEuler-Rodrigues parameters12b3fa6e1e79
addedQuaternion rotation advantage1d3e60241e18
addedQuaternion angle-axis extractioncbacc7a2f908
addedQuaternion interpolation6770983f758b
addedQuaternions avoid gimbal lockf3ae55114855
addedRotation matrix as first conversion step6ab119e5e3d8
addedOrientation by three elemental rotations0ab9d756ec20
addedRotation matrix decomposition108b5b5b08dc
addedRotation matrix convention example9dfc9e15aa7a
addedMatrix convention dependence4755e52f938e
addedColumn-vector matrix conventionb3580b52650f
addedActive rotation matrix conventionba0b25bc0eae
addedIntrinsic matrix convention955d9245e35c
addedRight-handed matrix convention21ba1cfd9646
addedElemental rotation matrices81e97e076263
addedSine and cosine abbreviationse005d210e237
addedPassive rotations by transposeb1833d2867cb
addedRotation matrix angle formulas8c8e76262965
addedEuler angles chart SO(3)28a51c92b069
addedEuler chart singularityff38b7e879ff
addedSpin(3) as hypersphere0c2ef809c292
addedSO(3) as real projective space30d78f60c405
addedTwo-to-one spin ambiguity3dd675c30168
addedSU(2) three-angle decomposition2daef0444433
addedSU(2) beta rangea8c795c12e15
addedSO(3) Haar measureedf02b7001ab
addedUniform random orientation generation74e583bd3e0e
addedGeometric algebra abstraction938cbb686e91
addedHigher-dimensional Euler analogues0b77b4957698
addedRotation about an axis fails in high dimensions7394e92878ce
addedRotation in a planeb1746adc993f
addedNumber of Euler angles for SO(n)d7f0926beb17
addedEuler angles and coordinate planesd2d09c7df799
addedSO(4) rotation matrix quaternions211f7ae815f7
addedSO(4) degrees of freedomea79dbc831ee
addedGimbal direct measurabilitye94549cda000
addedGyro and lab frame equivalence516f1c5db3c1
addedEuler angles directly measurable78e2acd23fe2
addedIntrinsic rotation requires multiple gimbalsfd3e91077b8b
addedSpace coordinates2e5d79d68af6
addedBody coordinates5d0dd5e3488c
addedBody-coordinate inertia tensor constancya04d08e994bf
addedPrincipal axesde259ba44ce4
addedAngular velocity in moving framebcc2c95f7a14
addedEuler rigid body equationsadf3b5a99922
addedCrystallographic texture by Euler angles8da11f0eac91
addedCrystallite orientation depictionaba933916bc0
addedBunge ZXZ convention4729943e7ad2
addedTexture passive rotations4f110eae389f
addedBunge matrix transpose5b7d435f828a
addedRobotics wrist degrees of freedom7d1014cc76b3
addedElectronic stability control36110135086f
addedCamera pointing in 3D modeling0ddbd5efdd4c
addedGun fire control corrections3ba83e768465
addedGun order Euler angle computationseed5f34787b4
addedAngular momentum quantum mechanicsb9412300fe71
addedSO(3) representations in quantum mechanics023fa3a051ec
addedEuler angles in SO(3) calculations680ad8e0ff04
addedMobile-device Euler angles0843db1b2da4
addedEuler-angle mobile applications758c9d2054e3