哈工大慣性技術(shù)考試題

1、Lecture 1 - Introduction1E1 2.3*Basic idea ( F ) The most important feature of an inertial navigation system is that its positioning errors are bounded.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 ) Inertial navigation is based on observation of celestial bodies.慣性導(dǎo)航是基于觀察天體。/*請(qǐng)以課件中的為準(zhǔn)，如果有誤請(qǐng)見(jiàn)諒。標(biāo)有疑問(wèn)的請(qǐng)以課件中的為準(zhǔn)，如果有誤請(qǐng)見(jiàn)諒。

2、標(biāo)有疑問(wèn)的地方請(qǐng)看課件地方請(qǐng)看課件*/Lecture 1 - Introduction2E1 3.1*Gyroscope ( F ) In a strapdown INS, the gyros can measure the rotation of the vehicle relative to the Earth.在捷聯(lián)式INS,陀螺儀可以測(cè)量載體相對(duì)于地球的自轉(zhuǎn)。Lecture 1 - Introduction3E1 5.1*Higher precision: ESG ( F ) Up to now, the type of gyroscope that has the highest p

3、recision is MEMS gyro.到現(xiàn)在為止，具有最高精度類(lèi)型的陀螺儀是到現(xiàn)在為止，具有最高精度類(lèi)型的陀螺儀是MEMS陀螺陀螺儀。儀。Lecture 1 - Introduction4E2 1.1*Earth: shape and gravity ( T ) On the surface of the Earth, the local gravity and the local gravitation are usually not in the same direction.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。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。

4、Lecture 1 - Introduction5E2 1.3*Earth: motion ( F ) The spinning rate of the Earth in the inertial space is 15 degrees/hour.地球的旋轉(zhuǎn)速度在慣性空間是15度/小時(shí)。Lecture 1 - Introduction6E2 2.2*Frame: Earth and Geographical ( T ) As a vehicle moves on the surface of the Earth, so does the origin of the local geograph

5、ical frame.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(wèn)）Lecture 1 - Introduction7 ( T ) As a vehicle is motionless on the surface of the Earth, its velocity in the inertial space can be written as , where R is the position of the vehicle in the Earth frame, and is the absolute spinning rate of the Earth.由于載體

6、靜止在地球的表面上，其在慣性空間的速度可以寫(xiě)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(xiě)為為 ，其中，其中R為載體在地球坐標(biāo)系的位置，為載體在地球坐標(biāo)系的位置， 是地球的絕是地球的絕對(duì)旋轉(zhuǎn)速率。對(duì)旋轉(zhuǎn)速率。E2 3.1*Transport velocityeReReeLecture 1 - Introduction8E2 3.3*Coriolis Theorem CoordinatedIf a vector B is coordinated in a rotating frame oxyz as如果一個(gè)向量B在旋轉(zhuǎn)坐標(biāo)系oxyz中分解為kBjBiBBzyx, then its rela

7、tive changing rate（相對(duì)變化的速度）in oxyz can be expressed as C .A.kdtdBjdtdBidtdBdtBdzyxdtkdBdtj dBdti dBdtBdzyxdtkdBdtj dBdti dBkdtdBjdtdBidtdBdtBdzyxzyxB.C.Lecture 1 - Introduction9E2 4.2*Angular Inertia matrix ( T ) The shape of the rotor of a spinning gyroscope is usually designed as symmetric. As a r

8、esult, the angular momentum of the rotor can be expressed in a much simplified form.一個(gè)旋轉(zhuǎn)的陀螺儀轉(zhuǎn)子的形狀通常設(shè)計(jì)為對(duì)稱(chēng)的。其結(jié)果是，一個(gè)旋轉(zhuǎn)的陀螺儀轉(zhuǎn)子的形狀通常設(shè)計(jì)為對(duì)稱(chēng)的。其結(jié)果是，轉(zhuǎn)子的角動(dòng)量可以用一個(gè)更簡(jiǎn)單的形式表示。轉(zhuǎn)子的角動(dòng)量可以用一個(gè)更簡(jiǎn)單的形式表示。Lecture 1 - Introduction10E2 4.3*Theorem of Angular Momentum ( T ) The angular momentum of a body will keep unchanging whe

9、n no torque is applied to it.當(dāng)沒(méi)有施加轉(zhuǎn)矩給物體時(shí)它的角動(dòng)量將保持不變。當(dāng)沒(méi)有施加轉(zhuǎn)矩給物體時(shí)它的角動(dòng)量將保持不變。Lecture 1 - Introduction11E3 2.3*Law of precessionThe angular rate of precession of a 2-DOF gyro is in the same direction as that of the applied torque.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。相同。( F )Lecture 1 - Introd

10、uction12E3 2.5*Direction of precessionTo make the spinning axis of a 2-DOF gyro rotate around its inner ring axis, a torque need to be applied along its B axis.為了使一個(gè)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)，自由度陀螺儀的旋轉(zhuǎn)軸繞其內(nèi)環(huán)軸旋轉(zhuǎn)，扭矩需要作用于扭矩需要作用于軸。軸。 inner ring B. outer ring C. spinning A.內(nèi)環(huán)內(nèi)環(huán) B.外環(huán)外環(huán) C.轉(zhuǎn)軸轉(zhuǎn)軸Lecture 1 - Intro

11、duction13E3 2.6*speed of precessionThe rate of precession of a 2-DOF gyro is proportional to its angular momentum.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。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 )Lecture 1 - Introduction14E3 3.1*Gyroscopic torque: definitionThe precession of a 2-DOF gyro is caused by gyroscopic torque.一個(gè)兩自由度陀螺儀的進(jìn)動(dòng)是

12、由陀螺力矩引起的。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 )Lecture 1 - Introduction15E3 4.3*Stability, Drift and NutationThe spinning axis of a powered 2-DOF gyro keeps stable in the inertial space under any condition.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。保持穩(wěn)定。( F )Lecture 1 - Introduction16E3 6.4*Summary

13、 of responsesAn impulse torque applied to a powered 2-DOF gyro causes merely its nutation, while a constant torque causes only its precession.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(huì)導(dǎo)致其進(jìn)動(dòng)。恒轉(zhuǎn)矩只會(huì)導(dǎo)致其進(jìn)動(dòng)。 ( F ) Lecture 1 - Introduction17E4 1.0*Single-DOF gyro: introThe spinning axis of a 1

14、-DOF gyro remains in the same direction no matter how the base rotates.無(wú)論基座怎樣轉(zhuǎn)動(dòng)一個(gè)單自由度陀螺儀的旋轉(zhuǎn)軸保持無(wú)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。在同一方向上。 ( F ) Lecture 1 - Introduction18E4 1.1*Sensing axisThe spinning axis of a 1-DOF gyro can not rotate relative to the base around its sensitive axis.一個(gè)單自由度陀螺儀的旋轉(zhuǎn)軸不能相對(duì)地圍繞其

15、敏感一個(gè)單自由度陀螺儀的旋轉(zhuǎn)軸不能相對(duì)地圍繞其敏感軸的基極旋轉(zhuǎn)。軸的基極旋轉(zhuǎn)。( T )Lecture 1 - Introduction19E4 3.2*Rate gyro and integrating gyroIn a 1-DOF rate gyro, there is a damper along its output axis, while in a 1-DOF integrating gyro, there is not.在在1自由度速率陀螺儀，有沿其輸出軸的閥門(mén)，而自由度速率陀螺儀，有沿其輸出軸的閥門(mén)，而1自由度自由度積分陀螺中則沒(méi)有此部件。積分陀螺中則沒(méi)有此部件。( F )Lec

16、ture 1 - Introduction20E4 3.3*Effect of command inputA command torque applied to a 1-DOF gyro produces the same response as a proportional input angular rate does.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)。速率相同的響應(yīng)。( T )Lecture 1 - Introduction21E5 2.1*Specific forceAs a rocket is being la

17、unched vertically, the accelerometer with upward sensitive axis has an output of 8g, where g is the magnitude of the local gravity acceleration. Then, the absolute upward acceleration of the rocket is C .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，其中其中g(shù)為當(dāng)?shù)刂亓铀俣?。然后，火箭的絕對(duì)向上的加速為當(dāng)?shù)刂亓铀俣?。然后，火箭的絕對(duì)向上的

18、加速度是度是A. 8g B. 7g C. 9g Lecture 1 - Introduction22E5 3.5*Error classificationThe precision of an inertial navigation system is mainly determined by that of its accelerometers.慣性導(dǎo)航系統(tǒng)的精度主要由它的加速度來(lái)確定。慣性導(dǎo)航系統(tǒng)的精度主要由它的加速度來(lái)確定。( F )Lecture 1 - Introduction23E5 4.1*EN frame rotationA missile is flying near the

19、 surface of the Earth with northward velocity , at latitude . The radius of the Earth is , and the spinning of the Earth can be ignored. For the inertial platform on the vehicle to keep up with the local geographical frame, the platform need to rotate in the inertial space at the angular rate C .導(dǎo)彈在

20、地球表面附導(dǎo)彈在地球表面附近飛行，有向北的速度近飛行，有向北的速度 ，緯度為，緯度為 。地球的半徑為。地球的半徑為 ，地球的自轉(zhuǎn)可，地球的自轉(zhuǎn)可以被忽略。為了使載體上的慣性平臺(tái)與當(dāng)?shù)氐牡乩碜鴺?biāo)系保持一致，平以被忽略。為了使載體上的慣性平臺(tái)與當(dāng)?shù)氐牡乩碜鴺?biāo)系保持一致，平臺(tái)需要在慣性空間中以臺(tái)需要在慣性空間中以的角速度旋轉(zhuǎn)的角速度旋轉(zhuǎn)NVRcosRVNsinRVNRVNtanRVN A. around the local north C. around the local west B. around the local east D. around the local upward NVRLec

21、ture 1 - Introduction24E5 4.4*detrimental accelerations*As a vehicle moves on the surface of the Earth, the outputs of the accelerometers on its inertial platform can be directly integrated to obtained the velocities of the vehicle relative to the Earth.載體在地球的表面運(yùn)動(dòng)時(shí)，其慣性平臺(tái)上的加速度計(jì)的輸載體在地球的表面運(yùn)動(dòng)時(shí)，其慣性平臺(tái)上的加速

22、度計(jì)的輸出可以被直接集成來(lái)獲得載體相對(duì)于地球的速度。出可以被直接集成來(lái)獲得載體相對(duì)于地球的速度。( F )Lecture 1 - Introduction25E6 2.0*Classification of INS*( F ) In a platform INS using local geographical mechanization, its inertial platform need to be kept stable in the inertial space.在當(dāng)?shù)氐牡乩頇C(jī)械化平臺(tái)慣導(dǎo)系統(tǒng)中，其慣性平臺(tái)在慣性在當(dāng)?shù)氐牡乩頇C(jī)械化平臺(tái)慣導(dǎo)系統(tǒng)中，其慣性平臺(tái)在慣性空間需要保持穩(wěn)定?？臻g

23、需要保持穩(wěn)定。Lecture 1 - Introduction26E6 3.8*Summary: updating proceduresWhen updating an inertial platform to follow the local geographical frame, which of the following jobs has to be done immediately after the velocities of the vehicle relative to the ground are obtained? C .在調(diào)整慣性平臺(tái)來(lái)適應(yīng)當(dāng)?shù)氐牡乩碜谡{(diào)整慣性平臺(tái)來(lái)適應(yīng)

24、當(dāng)?shù)氐牡乩碜鴺?biāo)系時(shí)，得到載體相對(duì)于地面的速度后下列哪項(xiàng)工作需要立即做？標(biāo)系時(shí)，得到載體相對(duì)于地面的速度后下列哪項(xiàng)工作需要立即做？A. to remove detrimental accelerations去除有害的加速度去除有害的加速度B. to sent command torques to the gyros on the platform發(fā)送命令轉(zhuǎn)矩到平發(fā)送命令轉(zhuǎn)矩到平臺(tái)上的陀螺儀臺(tái)上的陀螺儀C. to calculate the angular rates of the local geographical frame計(jì)算本地地計(jì)算本地地理坐標(biāo)系的角速率理坐標(biāo)系的角速率D. to se

25、nt the gyro outputs to motors on the platform gimbals發(fā)送陀螺儀輸發(fā)送陀螺儀輸出到支架平臺(tái)上的電機(jī)出到支架平臺(tái)上的電機(jī)Lecture 1 - Introduction27E6 4.5*Block-diagram( T ) If a platform INS based on inertial mechanization is used by a vehicle moving the surface of the Earth, then the platform need not follow the local geographical fr

26、ame.如果基于慣性機(jī)械化平臺(tái)如果基于慣性機(jī)械化平臺(tái)慣導(dǎo)系統(tǒng)應(yīng)用于在地表運(yùn)動(dòng)的慣導(dǎo)系統(tǒng)應(yīng)用于在地表運(yùn)動(dòng)的載體上，則該平臺(tái)不必遵循本地地理坐標(biāo)系。載體上，則該平臺(tái)不必遵循本地地理坐標(biāo)系。Lecture 1 - Introduction28E6 5.3*Gimbals: locking of 3-ringAn inertial navigation system using a 4-ring platform allows the vehicle to rotate freely.使用使用4 - 環(huán)平臺(tái)慣性導(dǎo)航系統(tǒng)允許環(huán)平臺(tái)慣性導(dǎo)航系統(tǒng)允許載體自由轉(zhuǎn)動(dòng)。載體自由轉(zhuǎn)動(dòng)。 ( T ) Lecture

27、1 - Introduction29E7 1.8*Questions answeredIf a command torque is added to one of the gyros on an inertial platform, the platform will rotate for an angle proportional to the torque.如果一個(gè)命令轉(zhuǎn)矩加到慣性平臺(tái)上的陀螺儀中的一個(gè)如果一個(gè)命令轉(zhuǎn)矩加到慣性平臺(tái)上的陀螺儀中的一個(gè)上面，該平臺(tái)將旋轉(zhuǎn)一個(gè)與轉(zhuǎn)矩成比例的角度。上面，該平臺(tái)將旋轉(zhuǎn)一個(gè)與轉(zhuǎn)矩成比例的角度。( F )Lecture 1 - Introduction3

28、0E7 2.6*Schuler tuning demystifiedWhat is the physical meaning of Shuler tuning?什么是舒勒調(diào)諧的物理意義？什么是舒勒調(diào)諧的物理意義？Please write out the conditions of Shuler tuning for the platform updating loop as shown in the block diagram.請(qǐng)請(qǐng)寫(xiě)出如框圖所示平臺(tái)更新循環(huán)的舒勒調(diào)諧條件。寫(xiě)出如框圖所示平臺(tái)更新循環(huán)的舒勒調(diào)諧條件。)(sVERs1)(cosses1NsKaRK1)(cossKe2KtItKYH

29、s1gLecture 1 - Introduction31E9 1.1*Strapdown INS: FeaturesWhich of the following features are shared by Platform INS and Strapdown INS? D .以下哪些以下哪些特征是平臺(tái)慣導(dǎo)和捷聯(lián)慣導(dǎo)共有的特征是平臺(tái)慣導(dǎo)和捷聯(lián)慣導(dǎo)共有的A. Accelerometers and gyros are fixed to the body of the vehicle加速度加速度計(jì)和陀螺儀被固定到計(jì)和陀螺儀被固定到載體上面載體上面B. Outputs of gyros are in

30、tegrated to obtain the attitude of the vehicle.陀螺儀的輸出被積分陀螺儀的輸出被積分用來(lái)獲得載體的姿態(tài)。用來(lái)獲得載體的姿態(tài)。C. There is a physical platform to emulate the navigation frame.有一有一個(gè)物理平臺(tái)來(lái)模擬導(dǎo)航個(gè)物理平臺(tái)來(lái)模擬導(dǎo)航坐標(biāo)系。坐標(biāo)系。D. In the navigation frame, accelerations are integrated to obtain the velocities and position of the vehicle.在導(dǎo)航坐標(biāo)系中，加

31、速度被在導(dǎo)航坐標(biāo)系中，加速度被集成以獲得載體的速度和位置。集成以獲得載體的速度和位置。Lecture 1 - Introduction32E9 2.3*Derivative of direction cosinesIf the attitude of a vehicle is described by a direction cosine matrix C, and its angular rate by whose skew symmetric matrix is , then C can be determined by solving the differential equation

32、B .如果一個(gè)如果一個(gè)載體的姿態(tài)是由方向余弦矩陣載體的姿態(tài)是由方向余弦矩陣C來(lái)描述，并且來(lái)描述，并且其角速度由其角速度由的斜對(duì)稱(chēng)矩陣的斜對(duì)稱(chēng)矩陣描述，那么描述，那么C可以通過(guò)求解可以通過(guò)求解微分方程微分方程確定確定CC A.B.C.D. CCCC21CC21Lecture 1 - Introduction33E9 3.7 ExampleA vehicle is equipped with SINS. At time n, its body frame coincides with the inertial frame, which is chosen as navigation frame.

33、Then from time n to n+1, the angular increment outputs of its three gyros GX, GY, GZ, are 0.002, 0.004 and 0.006 (rad) respectively; Please use 1st order Peano-Paker algorithm to compute the DCM from body frame to inertial frame at time n+1.載體載體配備捷聯(lián)慣導(dǎo)系統(tǒng)。在時(shí)間配備捷聯(lián)慣導(dǎo)系統(tǒng)。在時(shí)間n，它的機(jī)身，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

34、。再?gòu)淖鴺?biāo)系與慣性坐標(biāo)系重合，被選為導(dǎo)航坐標(biāo)系。再?gòu)臅r(shí)間時(shí)間n到到n +1，它的三個(gè)陀螺儀的角度增量輸出，它的三個(gè)陀螺儀的角度增量輸出GX ，GY，GZ，分別是分別是0.002，0.004和和0.006（弧度）（弧度）;請(qǐng)使用一階皮亞諾請(qǐng)使用一階皮亞諾-PAKER算法，計(jì)算在算法，計(jì)算在n +1時(shí)刻時(shí)刻從機(jī)身坐標(biāo)系到慣性系的從機(jī)身坐標(biāo)系到慣性系的DCM 。solution3)() 1(InCnCinitially)(nC3Iand000 xyxzyz0002. 0004. 0002. 00006. 0004. 0006. 00 ) 1(nCso0002. 0004. 0002. 00006.

35、0004. 0006. 0033IILecture 1 - Introduction34E10 1.1*Definition of quaternionsThe unit vectors of a frame XYZ are i, j, k respectively. If the frame rotates around its axis Z for 60 degrees, then this rotation can be described by a quaternion D .坐標(biāo)系坐標(biāo)系單位矢量單位矢量XYZ分別為分別為i，j，K。如果。如果坐標(biāo)系繞其軸線(xiàn)坐標(biāo)系繞其軸線(xiàn)Z旋轉(zhuǎn)旋轉(zhuǎn)60

36、度，則該旋轉(zhuǎn)可以通過(guò)一個(gè)四元數(shù)度，則該旋轉(zhuǎn)可以通過(guò)一個(gè)四元數(shù)描述描述223ik2321i4341k2123A. B. C. D.Lecture 1 - Introduction35E10 2.2* i, j, k in multiplicationkjiq0020Ifkjih2000andthenhq C .A.kji0400kji0004kji0400kji4000C.B.D.Lecture 1 - Introduction36E10 2.3-2.5*quaternion operationsIf q1, q2, and q3 are three normalized quaternions

37、, then D .如果如果Q1，Q2和和Q3是三種歸一化四元數(shù)，那么是三種歸一化四元數(shù)，那么1221qqqq312321)()(qqqqqq*2*1*21)(qqqq*111qqA.B.C.D.Lecture 1 - Introduction37E10 3.2*Rotation of frameA vector V is coordinated as in a fixed frame XYZ, and as in a rotating frame XYZ, where i, j, k and i, j, k are the unit vectors of XYZ and XYZ respec

38、tively. Denote as the image of V in XYZ, and as its image in XYZ.向量向量v在一個(gè)固定的框架在一個(gè)固定的框架XYZ中分解為中分解為 ，在旋轉(zhuǎn)框架，在旋轉(zhuǎn)框架XYZ中分解為中分解為 ，其中，其中i，j，k和和I，J，K分別是分別是XYZ和和XY Z的單位向量。的單位向量。記記 為為V在在XYZ的的像，像， 作為其在作為其在XYZ的的像。像。kjiVzyxVVVkjiVzyxVVVeVeVkjiVzyxeVVVkjiVzyxeVVVkjiVzyxeVVVkjiVzyxeVVVA.C.B.D.Then D .kjiVzyxVVVkjiV

39、zyxVVVeVeVLecture 1 - Introduction38E10 4.2*Combination: imageryThe body of a vehicle has made three successive rotations described, in the order of rotation, by quaternions q1, q2 and q3 respectively. If the rotating axes of q1, q2, q3 are all in imagery forms, then the combination of these rotatio

40、ns can be described by quaternion 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)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和和Q3分別描述。如果分別描述。如果Q1，Q2，Q3的旋轉(zhuǎn)軸都的旋轉(zhuǎn)軸都用意象用意象形式（翻譯不準(zhǔn)確，見(jiàn)諒），那么這些旋轉(zhuǎn)的組合可以通形式（翻譯不準(zhǔn)確，見(jiàn)諒），那么這些旋轉(zhuǎn)的組合可以通過(guò)四元數(shù)過(guò)四元數(shù) 描述描述 123qqqq ( F ) 123qqqqLecture 1 - Introduction39E10 5.0*Differential equation of quaternionsThe attitude of a ve

41、hicle is described by a quaternion q, and its angular rate by , then q can be determined by solving the differential equation D .載體的姿態(tài)是由四元數(shù)載體的姿態(tài)是由四元數(shù)q描述的，并且其角速度由描述的，并且其角速度由表示，表示，則則q可通過(guò)求解微分方程可通過(guò)求解微分方程來(lái)確定來(lái)確定qq qq21qq21qq A.B.C.D.Lecture 1 - Introduction40E10 5.2*ExampleA SINS is used in a vehicle. At

42、time n , the axis X of the vehicle frame points to the east, Y is 60 degrees above the north.捷聯(lián)慣導(dǎo)捷聯(lián)慣導(dǎo)系統(tǒng)應(yīng)用在載體上。在時(shí)間系統(tǒng)應(yīng)用在載體上。在時(shí)間n，載體坐標(biāo)系載體坐標(biāo)系X軸軸指向東部，指向東部，Y軸指向軸指向偏北偏北60度？（有疑問(wèn)，需要看課件）。度？（有疑問(wèn)，需要看課件）。Then, from time n to n+1, the angular increment outputs of its three gyros GX, GY, GZ, are 0.002, 0.004 and 0

43、.006 (rad) respectively.然后，從時(shí)間然后，從時(shí)間n到到n +1，它的三個(gè)陀螺儀，它的三個(gè)陀螺儀GX，GY，GZ，的角增量輸出，的角增量輸出分分別是別是0.002，0.004和和0.006（弧度）。（弧度）。Ignore the rotation of the geographical frame. Please use the first-order Peano-Paker algorithm to compute the quaternion from the geographical frame to the vehicle frame at time n+1.忽視

44、地理坐標(biāo)系的轉(zhuǎn)動(dòng)。請(qǐng)使用一階皮亞諾忽視地理坐標(biāo)系的轉(zhuǎn)動(dòng)。請(qǐng)使用一階皮亞諾PAKER算法計(jì)算在時(shí)間算法計(jì)算在時(shí)間n+1時(shí)時(shí)從地理坐標(biāo)系到載體坐標(biāo)系的四元數(shù)。從地理坐標(biāo)系到載體坐標(biāo)系的四元數(shù)。Lecture 1 - Introduction41E14 2.2*Optic path differenceIncreasing the size of a Sagnac interferometer can improve its sensitivity to an angular rate input.增大增大Sagnac增加干涉儀的尺寸可以提高其對(duì)角速率輸入的靈敏增加干涉儀的尺寸可以提高其對(duì)角速率輸入

45、的靈敏度。度。( T )Lecture 1 - Introduction42E14 3.4*Frequency differenceA laser gyro works by measuring the optic path difference between two beams of laser traveling in opposite directions within its resonance cavity. 激光陀螺儀的工作原理激光陀螺儀的工作原理是測(cè)量激光的兩個(gè)光束在諧振腔中是測(cè)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。沿相反的方向行進(jìn)的光路差。( F )Lectur

46、e 1 - Introduction43E14 3.5*ExampleA laser gyro has a triangular resonance cavity with perimeter 300mm, and the wavelength of the laser is 0.6328m. If the gyro is to measure the spinning rate of the Earth, which is 7.2910-5rad/s, please compute the frequency difference output of the gyro.一種激光陀螺儀有周長(zhǎng)一

47、種激光陀螺儀有周長(zhǎng)為為300毫米毫米的三角形諧振腔，激光的波長(zhǎng)為的三角形諧振腔，激光的波長(zhǎng)為0.6328m。如果陀螺儀。如果陀螺儀要測(cè)量地球的旋轉(zhuǎn)速率，即要測(cè)量地球的旋轉(zhuǎn)速率，即7.2910-5rad/ s，請(qǐng)計(jì)，請(qǐng)計(jì)算陀螺的頻率差輸出。算陀螺的頻率差輸出。Hint: the output of a laser gyro can be computed using提示：一個(gè)激光陀螺儀的輸出可使用提示：一個(gè)激光陀螺儀的輸出可使用如下的式子計(jì)算如下的式子計(jì)算LAV4Lecture 1 - Introduction44E14 5.1-5.4*Errors and solutionsIn a lase

48、r gyro, double anodes are employed to reduce the lock-in error caused by Langmuir flow.在一個(gè)激光陀螺儀在一個(gè)激光陀螺儀中，雙陽(yáng)極用來(lái)降低由朗繆爾流動(dòng)引中，雙陽(yáng)極用來(lái)降低由朗繆爾流動(dòng)引起的鎖定錯(cuò)誤。起的鎖定錯(cuò)誤。( F )Lecture 1 - Introduction45E15 2.2*Path differenceThe sensitivity of a fiber optic gyro to its input angular rate can be improved by increasing the rounds of its fiber coils. 一個(gè)光纖陀螺儀的輸入角速度的靈敏度可以通過(guò)增加一個(gè)光纖陀螺儀的輸入角速度的靈敏度可以通過(guò)增加其纖維線(xiàn)圈的其纖維線(xiàn)圈的圈數(shù)提高。