哈工大慣性技術(shù)考試題

Lecture1--Introduction1E12.3*Basicidea(F)Themostimportantfeatureofaninertialnavigationsystemisthatitspositioningerrorsarebounded.慣性導(dǎo)航系統(tǒng)的最重要的特性是它的定位誤差是有界的(F)Inertialnavigationisbasedonobservationofcelestialbodies.慣性導(dǎo)航是基于觀察天體。/*請以課件中的為準(zhǔn)，如果有誤請見諒。標(biāo)有疑問的地方請看課件*/Lecture1--Introduction2E13.1*Gyroscope(F)InastrapdownINS,thegyroscanmeasuretherotationofthevehiclerelativetotheEarth.在捷聯(lián)式INS,陀螺儀可以測量載體相對于地球的自轉(zhuǎn)。Lecture1--Introduction3E15.1*Higherprecision:ESG(F)Uptonow,thetypeofgyroscopethathasthehighestprecisionisMEMSgyro.到現(xiàn)在為止，具有最高精度類型的陀螺儀是MEMS陀螺儀。Lecture1--Introduction4E21.1*Earth:shapeandgravity(T)OnthesurfaceoftheEarth,thelocalgravityandthelocalgravitationareusuallynotinthesamedirection.在地球的表面，局部重力和本地引力通常不是在相同的方向。Lecture1--Introduction5E21.3*Earth:motion(F)ThespinningrateoftheEarthintheinertialspaceis15degrees/hour.地球的旋轉(zhuǎn)速度在慣性空間是15度/小時。Lecture1--Introduction6E22.2*Frame:EarthandGeographical(T)AsavehiclemovesonthesurfaceoftheEarth,sodoestheoriginofthelocalgeographicalframe.當(dāng)載體在地球的表面運動，當(dāng)?shù)氐牡乩碜鴺?biāo)系的原點也在此。（不通順，有疑問）Lecture1--Introduction7(T)AsavehicleismotionlessonthesurfaceoftheEarth,itsvelocityintheinertialspacecanbewrittenas,whereRisthepositionofthevehicleintheEarthframe,andistheabsolutespinningrateoftheEarth.由于載體靜止在地球的表面上，其在慣性空間的速度可以寫為，其中R為載體在地球坐標(biāo)系的位置，是地球的絕對旋轉(zhuǎn)速率。E23.1*TransportvelocityLecture1--Introduction8E23.3*CoriolisTheoremCoordinatedIfavectorBiscoordinatedinarotatingframeoxyzas如果一個向量B在旋轉(zhuǎn)坐標(biāo)系oxyz中分解為,thenitsrelativechangingrate（相對變化的速度）inoxyzcanbeexpressedasC.A.B.C.Lecture1--Introduction9E24.2*AngularInertiamatrix(T)Theshapeoftherotorofaspinninggyroscopeisusuallydesignedassymmetric.Asaresult,theangularmomentumoftherotorcanbeexpressedinamuchsimplifiedform.一個旋轉(zhuǎn)的陀螺儀轉(zhuǎn)子的形狀通常設(shè)計為對稱的。其結(jié)果是，轉(zhuǎn)子的角動量可以用一個更簡單的形式表示。Lecture1--Introduction10E24.3*TheoremofAngularMomentum(T)Theangularmomentumofabodywillkeepunchangingwhennotorqueisappliedtoit.當(dāng)沒有施加轉(zhuǎn)矩給物體時它的角動量將保持不變。Lecture1--Introduction11E32.3*LawofprecessionTheangularrateofprecessionofa2-DOFgyroisinthesamedirectionasthatoftheappliedtorque.一個兩自由度陀螺進(jìn)動的角速度與所施加的扭矩方向相同。(F)Lecture1--Introduction12E32.5*DirectionofprecessionTomakethespinningaxisofa2-DOFgyrorotatearounditsinnerringaxis,atorqueneedtobeappliedalongitsBaxis.為了使一個2自由度陀螺儀的旋轉(zhuǎn)軸繞其內(nèi)環(huán)軸旋轉(zhuǎn)，扭矩需要作用于——軸。innerringB.outerringC.spinningA.內(nèi)環(huán)B.外環(huán)C.轉(zhuǎn)軸Lecture1--Introduction13E32.6*speedofprecessionTherateofprecessionofa2-DOFgyroisproportionaltoitsangularmomentum.一個兩自由度陀螺進(jìn)動的速率正比于它的角動量。(F)Lecture1--Introduction14E33.1*Gyroscopictorque:definitionTheprecessionofa2-DOFgyroiscausedbygyroscopictorque.一個兩自由度陀螺儀的進(jìn)動是由陀螺力矩引起的。(F)Lecture1--Introduction15E34.3*Stability,DriftandNutationThespinningaxisofapowered2-DOFgyrokeepsstableintheinertialspaceunderanycondition.有源二自由度陀螺儀的旋轉(zhuǎn)軸在慣性空間中的任何情況下保持穩(wěn)定。(F)Lecture1--Introduction16E36.4*SummaryofresponsesAnimpulsetorqueappliedtoapowered2-DOFgyrocausesmerelyitsnutation,whileaconstanttorquecausesonlyitsprecession.施加在有源二自由度陀螺儀的脈沖扭矩只是使其章動，而恒轉(zhuǎn)矩只會導(dǎo)致其進(jìn)動。(F)Lecture1--Introduction17E41.0*Single-DOFgyro:introThespinningaxisofa1-DOFgyroremainsinthesamedirectionnomatterhowthebaserotates.無論基座怎樣轉(zhuǎn)動一個單自由度陀螺儀的旋轉(zhuǎn)軸保持在同一方向上。(F)Lecture1--Introduction18E41.1*SensingaxisThespinningaxisofa1-DOFgyrocannotrotaterelativetothebasearounditssensitiveaxis.一個單自由度陀螺儀的旋轉(zhuǎn)軸不能相對地圍繞其敏感軸的基極旋轉(zhuǎn)。(T)Lecture1--Introduction19E43.2*RategyroandintegratinggyroIna1-DOFrategyro,thereisadamperalongitsoutputaxis,whileina1-DOFintegratinggyro,thereisnot.在1自由度速率陀螺儀，有沿其輸出軸的閥門，而1自由度積分陀螺中則沒有此部件。(F)Lecture1--Introduction20E43.3*EffectofcommandinputAcommandtorqueappliedtoa1-DOFgyroproducesthesameresponseasaproportionalinputangularratedoes.運用于單自由度陀螺儀的指示轉(zhuǎn)矩產(chǎn)生與比例輸入角速率相同的響應(yīng)。(T)Lecture1--Introduction21E52.1*SpecificforceAsarocketisbeinglaunchedvertically,theaccelerometerwithupwardsensitiveaxishasanoutputof8g,wheregisthemagnitudeofthelocalgravityacceleration.Then,theabsoluteupwardaccelerationoftherocketisC.當(dāng)火箭正在垂直發(fā)射時，向上敏感軸加速度計輸出是8G，其中g(shù)為當(dāng)?shù)刂亓铀俣?。然后，火箭的絕對向上的加速度是A.8gB.7gC.9g

Lecture1--Introduction22E53.5*ErrorclassificationTheprecisionofaninertialnavigationsystemismainlydeterminedbythatofitsaccelerometers.慣性導(dǎo)航系統(tǒng)的精度主要由它的加速度來確定。(F)Lecture1--Introduction23E54.1*ENζframerotationAmissileisflyingnearthesurfaceoftheEarthwithnorthwardvelocity,atlatitude.TheradiusoftheEarthis,andthespinningoftheEarthcanbeignored.Fortheinertialplatformonthevehicletokeepupwiththelocalgeographicalframe,theplatformneedtorotateintheinertialspaceattheangularrateC.導(dǎo)彈在地球表面附近飛行，有向北的速度，緯度為。地球的半徑為，地球的自轉(zhuǎn)可以被忽略。為了使載體上的慣性平臺與當(dāng)?shù)氐牡乩碜鴺?biāo)系保持一致，平臺需要在慣性空間中以——的角速度旋轉(zhuǎn)A.aroundthelocalnorth

C.aroundthelocalwest

B.aroundthelocaleast

D.aroundthelocalupward

Lecture1--Introduction24E54.4*detrimentalaccelerations*AsavehiclemovesonthesurfaceoftheEarth,theoutputsoftheaccelerometersonitsinertialplatformcanbedirectlyintegratedtoobtainedthevelocitiesofthevehiclerelativetotheEarth.載體在地球的表面運動時，其慣性平臺上的加速度計的輸出可以被直接集成來獲得載體相對于地球的速度。(F)Lecture1--Introduction25E62.0*ClassificationofINS*(F)InaplatformINSusinglocalgeographicalmechanization,itsinertialplatformneedtobekeptstableintheinertialspace.在當(dāng)?shù)氐牡乩頇C(jī)械化平臺慣導(dǎo)系統(tǒng)中，其慣性平臺在慣性空間需要保持穩(wěn)定。Lecture1--Introduction26E63.8*Summary:updatingproceduresWhenupdatinganinertialplatformtofollowthelocalgeographicalframe,whichofthefollowingjobshastobedoneimmediatelyafterthevelocitiesofthevehiclerelativetothegroundareobtained?C.在調(diào)整慣性平臺來適應(yīng)當(dāng)?shù)氐牡乩碜鴺?biāo)系時，得到載體相對于地面的速度后下列哪項工作需要立即做？A.toremovedetrimentalaccelerations去除有害的加速度B.tosentcommandtorquestothegyrosontheplatform發(fā)送命令轉(zhuǎn)矩到平臺上的陀螺儀C.tocalculatetheangularratesofthelocalgeographicalframe計算本地地理坐標(biāo)系的角速率D.tosentthegyrooutputstomotorsontheplatformgimbals發(fā)送陀螺儀輸出到支架平臺上的電機(jī)Lecture1--Introduction27E64.5*Block-diagram(T)IfaplatformINSbasedoninertialmechanizationisusedbyavehiclemovingthesurfaceoftheEarth,thentheplatformneednotfollowthelocalgeographicalframe.如果基于慣性機(jī)械化平臺慣導(dǎo)系統(tǒng)應(yīng)用于在地表運動的載體上，則該平臺不必遵循本地地理坐標(biāo)系。Lecture1--Introduction28E65.3*Gimbals:lockingof3-ringAninertialnavigationsystemusinga4-ringplatformallowsthevehicletorotatefreely.使用4-環(huán)平臺慣性導(dǎo)航系統(tǒng)允許載體自由轉(zhuǎn)動。(T)Lecture1--Introduction29E71.8*QuestionsansweredIfacommandtorqueisaddedtooneofthegyrosonaninertialplatform,theplatformwillrotateforanangleproportionaltothetorque.如果一個命令轉(zhuǎn)矩加到慣性平臺上的陀螺儀中的一個上面，該平臺將旋轉(zhuǎn)一個與轉(zhuǎn)矩成比例的角度。(F)Lecture1--Introduction30E72.6*SchulertuningdemystifiedWhatisthephysicalmeaningofShulertuning?什么是舒勒調(diào)諧的物理意義？PleasewriteouttheconditionsofShulertuningfortheplatformupdatingloopasshownintheblockdiagram.請寫出如框圖所示平臺更新循環(huán)的舒勒調(diào)諧條件。Lecture1--Introduction31E91.1*StrapdownINS:FeaturesWhichofthefollowingfeaturesaresharedbyPlatformINSandStrapdownINS?D.以下哪些特征是平臺慣導(dǎo)和捷聯(lián)慣導(dǎo)共有的A.Accelerometersandgyrosarefixedtothebodyofthevehicle加速度計和陀螺儀被固定到載體上面B.Outputsofgyrosareintegratedtoobtaintheattitudeofthevehicle.陀螺儀的輸出被積分用來獲得載體的姿態(tài)。C.Thereisaphysicalplatformtoemulatethenavigationframe.有一個物理平臺來模擬導(dǎo)航坐標(biāo)系。D.Inthenavigationframe,accelerationsareintegratedtoobtainthevelocitiesandpositionofthevehicle.在導(dǎo)航坐標(biāo)系中，加速度被集成以獲得載體的速度和位置。Lecture1--Introduction32E92.3*DerivativeofdirectioncosinesIftheattitudeofavehicleisdescribedbyadirectioncosinematrixC,anditsangularratebyωwhoseskewsymmetricmatrixisΩ,thenCcanbedeterminedbysolvingthedifferentialequationB.如果一個載體的姿態(tài)是由方向余弦矩陣C來描述，并且其角速度由ω的斜對稱矩陣Ω描述，那么C可以通過求解微分方程——確定A.B.C.D.Lecture1--Introduction33E93.7ExampleAvehicleisequippedwithSINS.Attimen,itsbodyframecoincideswiththeinertialframe,whichischosenasnavigationframe.Thenfromtimenton+1,theangularincrementoutputsofitsthreegyrosGX,GY,GZ,are0.002,0.004and0.006(rad)respectively;Pleaseuse1storderPeano-PakeralgorithmtocomputetheDCMfrombodyframetoinertialframeattimen+1.載體配備捷聯(lián)慣導(dǎo)系統(tǒng)。在時間n，它的機(jī)身坐標(biāo)系與慣性坐標(biāo)系重合，被選為導(dǎo)航坐標(biāo)系。再從時間n到n+1，它的三個陀螺儀的角度增量輸出GX，GY，GZ，分別是0.002，0.004和0.006（弧度）;請使用一階皮亞諾-PAKER算法，計算在n+1時刻從機(jī)身坐標(biāo)系到慣性系的DCM。solutioninitiallyandsoLecture1--Introduction34E101.1*DefinitionofquaternionsTheunitvectorsofaframeXYZarei,j,krespectively.IftheframerotatesarounditsaxisZfor60degrees,thenthisrotationcanbedescribedbyaquaternionD.坐標(biāo)系單位矢量XYZ分別為i，j，K。如果坐標(biāo)系繞其軸線Z旋轉(zhuǎn)60度，則該旋轉(zhuǎn)可以通過一個四元數(shù)——描述A.B.C.D.Lecture1--Introduction35E102.2*i,j,kinmultiplicationIfandthenC.A.C.B.D.Lecture1--Introduction36E102.3-2.5*quaternionoperationsIfq1,q2,andq3arethreenormalizedquaternions,thenD.如果Q1，Q2和Q3是三種歸一化四元數(shù)，那么——A.B.C.D.Lecture1--Introduction37E103.2*RotationofframeAvectorViscoordinatedasinafixedframeXYZ,andasinarotatingframeX’Y’Z’,wherei,j,kandi’,j’,k’aretheunitvectorsofXYZandX’Y’Z’respectively.DenoteastheimageofVinX’Y’Z’,andasitsimageinXYZ.向量v在一個固定的框架XYZ中分解為，在旋轉(zhuǎn)框架X‘Y’Z‘中分解為，其中i，j，k和I’，J‘，K’分別是XYZ和X‘Y’Z‘的單位向量。

記為V在X’Y‘Z’的像，作為其在XYZ的像。A.C.B.D.ThenD.Lecture1--Introduction38E104.2*Combination:imageryThebodyofavehiclehasmadethreesuccessiverotationsdescribed,intheorderofrotation,byquaternionsq1,q2andq3respectively.Iftherotatingaxesofq1,q2,q3areallinimageryforms,thenthecombinationoftheserotationscanbedescribedbyquaternion載體已經(jīng)作了三次連續(xù)旋轉(zhuǎn)，旋轉(zhuǎn)的順序由四元數(shù)Q1，Q2和Q3分別描述。如果Q1，Q2，Q3的旋轉(zhuǎn)軸都用意象形式（翻譯不準(zhǔn)確，見諒），那么這些旋轉(zhuǎn)的組合可以通過四元數(shù)

描述

(F)Lecture1--Introduction39E105.0*DifferentialequationofquaternionsTheattitudeofavehicleisdescribedbyaquaternionq,anditsangularratebyω,thenqcanbedeterminedbysolvingthedifferentialequationD.載體的姿態(tài)是由四元數(shù)q描述的，并且其角速度由ω表示，則q可通過求解微分方程——來確定A.B.C.D.Lecture1--Introduction40E105.2*ExampleASINSisusedinavehicle.Attimen,theaxisXofthevehicleframepointstotheeast,Yis60degreesabovethenorth.捷聯(lián)慣導(dǎo)系統(tǒng)應(yīng)用在載體上。在時間n，載體坐標(biāo)系X軸指向東部，Y軸指向偏北60度？（有疑問，需要看課件）。Then,fromtimenton+1,theangularincrementoutputsofitsthreegyrosGX,GY,GZ,are0.002,0.004and0.006(rad)respectively.然后，從時間n到n+1，它的三個陀螺儀GX，GY，GZ，的角增量輸出分別是0.002，0.004和0.006（弧度）。Ignoretherotationofthegeographicalframe.Pleaseusethefirst-orderPeano-Pakeralgorithmtocomputethequaternionfromthegeographicalframetothevehicleframeattimen+1.忽視地理坐標(biāo)系的轉(zhuǎn)動。請使用一階皮亞諾PAKER算法計算在時間n+1時從地理坐標(biāo)系到載體坐標(biāo)系的四元數(shù)。Lecture1--Introduction41E142.2*OpticpathdifferenceIncreasingthesizeofaSagnacinterferometercanimproveitssensitivitytoanangularrateinput.增大Sagnac增加干涉儀的尺寸可以提高其對角速率輸入的靈敏度。(T)Lecture1--Introduction42E143.4*FrequencydifferenceAlasergyroworksbymeasuringtheopticpathdifferencebetweentwobeamsoflasertravelinginoppositedirectionswithinitsresonancecavity.激光陀螺儀的工作原理是測量激光的兩個光束在諧振腔中沿相反的方向行進(jìn)的光路差。(F)Lecture1--Introduction43E143.5*ExampleAlasergyrohasatriangularresonancecavitywithperimeter300mm,andthewavelengthofthelaseris0.6328μm.IfthegyroistomeasurethespinningrateoftheEarth,whichis7.29×10-5rad/s,pleasecomputethefrequencydifferenceoutputofthegyro.一種激光陀螺儀有周長為300毫米的三角形諧振腔，激光的波長為0.6328μm。如果陀螺儀要測量地球的旋轉(zhuǎn)速率，即7.29×10-5rad/s，請計算陀螺的頻率差輸出。Hint:theoutputofalasergyrocanbecomputedusing提示：一個激光陀螺儀的輸出可使用如下的式子計算Lecture1--Introduction44E145.1-5.4*ErrorsandsolutionsInalasergyro,doubleanodesareemployedtoreducethelock-inerrorcausedbyLangmuirflow.在一個激光陀螺儀中，雙陽極用來降低由朗繆爾流動引起的鎖定錯誤。(F)Lecture1--Introduction45E152.2*PathdifferenceThesensitivityofafiberopticgyrotoitsinputangularratecanbeimprovedbyincreasingtheroundsofitsfibercoils.一個光纖陀螺儀的輸入角速度的靈敏度可以通過增加其纖維線圈的圈數(shù)提高。(T)