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(shí)。Lecture1--Introduction6E22.2*Frame:EarthandGeographical(T)AsavehiclemovesonthesurfaceoftheEarth,sodoestheoriginofthelocalgeographicalframe.當(dāng)載體在地球的表面運(yùn)動(dòng)，當(dāng)?shù)氐牡乩碜鴺?biāo)系的原點(diǎn)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(gè)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(gè)旋轉(zhuǎn)的陀螺儀轉(zhuǎn)子的形狀通常設(shè)計(jì)為對稱的。其結(jié)果是，轉(zhuǎn)子的角動(dòng)量可以用一個(gè)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(shí)它的角動(dòng)量將保持不變。Lecture1--Introduction11E32.3*LawofprecessionTheangularrateofprecessionofa2-DOFgyroisinthesamedirectionasthatoftheappliedtorque.一個(gè)兩自由度陀螺進(jìn)動(dòng)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(gè)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(gè)兩自由度陀螺進(jìn)動(dòng)的速率正比于它的角動(dòng)量。(F)Lecture1--Introduction14E33.1*Gyroscopictorque:definitionTheprecessionofa2-DOFgyroiscausedbygyroscopictorque.一個(gè)兩自由度陀螺儀的進(jìn)動(dòng)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(dòng)，而恒轉(zhuǎn)矩只會導(dǎo)致其進(jìn)動(dòng)。(F)Lecture1--Introduction17E41.0*Single-DOFgyro:introThespinningaxisofa1-DOFgyroremainsinthesamedirectionnomatterhowthebaserotates.無論基座怎樣轉(zhuǎn)動(dòng)一個(gè)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(gè)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(yùn)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(shí)，向上敏感軸加速度計(jì)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(yùn)動(dòng)時(shí)，其慣性平臺上的加速度計(jì)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(shí)，得到載體相對于地面的速度后下列哪項(xiàng)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(jì)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(yùn)動(dòng)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(dòng)。(T)Lecture1--Introduction29E71.8*QuestionsansweredIfacommandtorqueisaddedtooneofthegyrosonaninertialplatform,theplatformwillrotateforanangleproportionaltothetorque.如果一個(gè)命令轉(zhuǎn)矩加到慣性平臺上的陀螺儀中的一個(gè)上面，該平臺將旋轉(zhuǎn)一個(gè)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(jì)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(gè)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(gè)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(shí)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(shí)間n到n+1，它的三個(gè)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(jì)算在n+1時(shí)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(gè)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(gè)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(shí)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(shí)間n到n+1，它的三個(gè)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(dòng)。請使用一階皮亞諾PAKER算法計(jì)算在時(shí)間n+1時(shí)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(gè)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(jì)算陀螺的頻率差輸出。Hint:theoutputofalasergyrocanbecomputedusing提示：一個(gè)激光陀螺儀的輸出可使用如下的式子計(jì)算Lecture1--Introduction44E145.1-5.4*ErrorsandsolutionsInalasergyro,doubleanodesareemployedtoreducethelock-inerrorcausedbyLangmuirflow.在一個(gè)激光陀螺儀中，雙陽極用來降低由朗繆爾流動(dòng)引起的鎖定錯(cuò)誤。(F)Lecture1--Introduction45E152.2*PathdifferenceThesensitivityofafiberopticgyrotoitsinputangularratecanbeimprovedbyincreasingtheroundsofitsfibercoils.一個(gè)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)