哈工大惯性技术考试例题

1.1 (F) The most important feature of an inertial navigation system is that its positioning errors are bounded.

(×)一个惯性导航系统最重要的特点是定位误差有界。自主autonomous or self-contained (F) Inertial navigation is based on observation of celestial bodies.

(×)惯性导航基于对天体的观察。牛顿第二定律based on Newton ’s second laws

1.2 (F) In a strapdown INS, the accelerometers can measure the acceleration of the vehicle relative to the surface of the Earth.

(×)在捷联式INS 中，加速度计可以测量载体相对于地球表面的加速度。相对于惯性空间

1.3 (F) Up to now, the type of gyroscope that has the highest precision is MEMS gyro.

(×)迄今为止，拥有最高精度的陀螺仪是MEMS 陀螺。Electrically suspended gyro=ESG

2.1 (T) On the surface of the Earth, the direction of the local gravity is usually different from that of the local gravitation.

(√)在地球表面，当地重力的方向通常不同于该处万有引力的方向。

2.2 (F) The absolute spinning rate of the Earth in the inertial space is 15 degrees per hour. (×)相对惯性空间，地球的绝对自转速度是15°/h 。 15.04107°/h

2.3 (T) As a vehicle moves on the surface of the Earth, the origin of the local geographical frame moves on the surface too.

(√)当载体在地球表面运动时，原始地理坐标系也在地球表面运动。

2.4 (T) A vehicle is staying motionless on the surface of the Earth. It is known that the position of the vehicle in the Earth frame is R, and the spinning rate of the earth in the inertial space is εω, then the velocity of the vehicle in the inertial space can be written as R e ?ω

(√)一个载体在地球表面保持静止，已知载体在地球坐标系中的位置为R ，地球在惯性中间的自转速度为w ，那么载体在惯性空间的速度可以写为w*R 。

2.5 If a vector B is coordinated in a rotating frame oxyz as →

→→++=k B j B i B B z y x , then the relative changing rate of the vector B in the rotating frame can be expressed in this frame as C. 如果一个向量B 在动坐标系中分解为，那么向量B 在动坐标系中的相对速度为C 。 A. y x z x y z dB dB dB dB di dj dk i j k B B B dt dt dt dt dt dt dt

=+++++ B. x y z dB di dj dk B B B dt dt dt dt

=++ C. y x z dB dB dB dB i j k dt dt dt dt

=++ 2.6 (T) The Coriolis acceleration of an object is caused by the interaction between the rotation of a transport frame and the relative motion of the object within the transport frame.

(√)一个物体的柯氏加速度由相对坐标系的旋转和物体在相对坐标系中的相对运动相互作用引起。

2.7 (T) The shape of the rotor of a spinning gyroscope is usually designed as symmetric. A benefit of such design is that the expression of the angular momentum of the rotor can be much simplified.

(√)一个旋转陀螺仪的转子形状通常设计为对称的。这种设计的好处是转子动量矩的表达式可以大大简化。

2.8 (T) The angular momentum of a body will keep unchanging when no torque is applied on it. (√)当没有力矩作用在物体上时，物体的动量矩保持不变。

3.1 (F) The angular rate of precession of a 2-DOF gyro is in the same direction as that of the applied torque.

(×)二自由度陀螺仪的进动角速度的方向和施加的力矩方向相同。 Perpendicular 正交

3.2 (F) To make the spinning axis of a 2-DOF gyro rotate around its outer ring axis, a torque need to be applied along the spinning axis.

(×)为使2-DOF 陀螺仪的转子轴绕外环轴转动，需在转子轴上施加力矩。inner 内环轴 To 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. 转子轴绕内环轴转动，需在外环轴施加力矩。

A. inner ring

B. outer ring

C. spinning

3.3 (F) The precession rate of a 2-DOF gyro is proportional to its angular momentum.

(×)二自由度陀螺仪的进动速度和它的动量矩成正比。 inverse proportional 反比

3.4 (F) The precession of a 2-DOF gyro is caused by gyroscopic torque.

(×)二自由度陀螺仪的进度是由陀螺力矩引起的。 applied torque 外加力矩

3.5 (F) The spinning axis of a powered 2-DOF gyro keeps stable in the inertial space under any condition.

(×)转动的2-DOF 陀螺仪的转子轴在任何情况下都在惯性空间保持稳定。tendency to keep

3.6 (T) The frequency of the nutation of a 2-DOF gyro is of the same order of magnitude as the spinning rate of its rotor.

(√)2-DOF 陀螺仪的章动频率与其转子的转动速率是相同的数量级。

Hints 提示

2

20x y H J J ω= 0x y e J J J e

x y H H J J J ω==== z H J γ≈ z

H J γ≈ 3.1 Which of the following types of torque has the largest impact on the precision of a 2-DOF gyro? B 下列哪种类型的力矩对2-DOF 的精度影响最大？ 常值>正弦>冲击

A. impulse torque 冲击

B. constant torque 常值

C. sinusoidal torque 正弦

3.2 (F) If a powered 2-DOF gyro is subject to an impulse torque, its response contains merely nutation; if the gyro is subject to a constant torque, its response contains merely precession. (×)如果一个转动的2-DOF 陀螺仪受到冲击力矩，响应只包括章动；受到常值力矩，响应只包括进动。常值：章动+进动

4.1 (F) The spinning axis of a 1-DOF gyro remains in the same direction no matter how the base rotates.

(×)无论基座怎么转动，1-DOF 陀螺仪的转子轴保持相同的方向。 绕y 轴进动

4.2 (T) The sensitive axis of a 1-DOF gyro is in the direction where the spinning axis has no degree of freedom relative to the base.

(√)1-DOF 陀螺仪的敏感轴沿着转子轴相对基座没有自由度的那个方向。

4.3 (F) The structural difference between a 1-DOF rate gyro and a 1-DOF integrating gyro is that:

in a rate gyro, there is a dumper along its output axis, while in an integrating gyro, there is no dumper along its output axis.

(×)单自由度的速率陀螺和积分陀螺结构上的区别是：速率陀螺沿输出轴有一个漏斗而积分陀螺没有。

4.4 (T) Adding a command torque along the output axis of a 1-DOF gyro is equivalent to adding a proportional angular rate along its input axis.

(√)沿单自由度陀螺仪的输出轴施加控制力矩相当于沿输入轴施加相应比例的角速率。

5.1 As a rocket is being launched vertically, the accelerometer whose sensitive axis is pointing upward has an output of 8g, where g is a unit of the local gravity acceleration, defined as positive upward. Then, the absolute upward acceleration of the rocket is B.

当一个火箭垂直发射，敏感轴指向上方的加速度计输出为8g ，定义为向上，g 是当地重力加速度的单位。那么，火箭的绝对加速度为7g 。

A. 8g

B. 7g

C. 9g

5.2 (F) The precision of an inertial navigation system (INS) is mainly determined by that of its accelerometers.

(×)一个惯性系统的精度主要取决于其加速度计的精度。 器件误差和初始误差

5.3 A missile is flying near the surface of the earth with northward velocity N V , at latitude ?. The radius of the Earth is R, 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

一个导弹在地球表面以速度N V 向北飞行，纬度为?。地球半径为R ，自转忽略。对于载体上的惯性平台若想跟踪地理坐标系，平台在惯性空间的转动角速度需为C 。 A. ?

cos R V N around the local north B.

?sin R V N around the local east C.

R

V N around the local west D. ?tan R V N around the local upward 5.4 (T) From the outputs of accelerometers along the local east-north-up, the influence of gravity and detrimental accelerations have to be compensated before these outputs are integrated to obtain the velocities of the vehicle relative to the ground.

(√)在地理坐标系加速度计的输出中，重力加速度和有害加速度的影响在这些输出被积分来获得载体相对地面的速度之前必须得到补偿。

6.1 In the updating loop of an inertial platform following the local geographical frame, which of the following jobs has to be done immediately after the velocities of the vehicle relative to the ground have been obtained? C

在跟踪地理坐标系的惯性平台的修正回路中，得到载体相对地面的速度后要进行哪一步

A. to remove detrimental accelerations 有害加速度补偿

B. to sent command torques to the gyros on the platform 施加陀螺力矩

C. to calculate the angular rates of the local geographical frame 计算地理坐标系的角速度

D. to sent the gyro outputs to motors on the platform gimbals 陀螺输出→控制平台框的电机

6.2 (T) An inertial navigation system using a 4-ring platform allows the vehicle to rotate freely. (√)一个惯性系统采用四环平台是为了载体自由转动。

7.1 1.10*Questions answered （PPT1.10） How well can the platform resist external disturbance? 121/YS

fY M C C H C

α= How do gyro errors affect the precision of platform? fX YS M H α

-= How is a command rate transferred to the platform? B YS M H

α

-= Is the system stable? ()G s 7.2 (F) If 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.

(×)给惯性平台的一个陀螺施加力矩，平台将转动一个适当的角度。

7.3What is the physical meaning of Shuler tuning? (简答题PPT2.7)

Please write out the conditions of Shuler tuning for the platform updating loop as shown in the block diagram.

Simply the gain-matching between real word channel and artificial channel of platform, to eliminate the contribution of acceleration and earth spinning to platform tracking error.

实质上是为了修正惯导平台（人工通道）永远跟踪上真实地理坐标系（现实通道）的转动，而对修正回路（人工通道）的增益参数进行调节，使之与现实通道对应的增益匹配的过程 a 12K t K K K H = 2K t K K H

?= 9.1 Which of the following features are shared by Platform INS and Strapdown INS? D. 下列哪种特征是平台惯导系统和捷联惯导系统共有的？D

A. Accelerometers and gyros are fixed to the body of the vehicle 加速度计和陀螺与载体固连

B. Outputs of gyros are integrated to determined the attitude of the vehicle.

对陀螺仪的输出进行积分，获取载体的姿态信息

C. There is a physical platform to emulate the navigation frame.

有一个物理平台来模拟导航坐标系

D. In the navigation frame, accelerations are integrated to obtain the velocities and position of the vehicle. 在导航坐标系中，加速度被积分来获得载体的速度和位置信息

9.2 The attitude of a vehicle is described by a direction cosine matrix C, and its angular rate by ω. And Ωis the skew symmetric matrix defined by ω. Then C can be determined by solving the differential equation B.

载体的姿态用方向余弦矩阵C 来表示，角速度为ω，Ω是斜对称矩阵，那么C 可以通过解微分方程B 来确定。

A. C C ω=

B. C C =Ω

C. 12C C ω=

D. 12

C C =Ω

9.3 At time n, the body frame of a vehicle using SINS coincides with the inertial frame, which is chosen as navigation frame. Then from time n to n+1, the angular increment outputs of its three gyros X, Y , Z, are 0.002, 0.004 and 0.006 (rad) respectively; Please use the first-order Peano-Paker algorithm to compute the DCM from body frame to inertial frame at time n+1. 某捷联惯导系统在 n 时刻，其载体坐标系和惯性坐标系重合。然后从时刻n 到时刻n+1,沿着载体三个轴的三个陀螺仪X,Y,Z 的角增量输出分别为0.002,0.004和0.006 (rad)；请利用基于Peano-Paker 解的一阶角增量算法计算时刻n+1载体和惯性坐标系之间的方向余弦矩阵。

Initially 3()C n I =

solution []3(1)()C n C n I +=+?Θ

Where 000.0060.00400.00600.00200.0040.0020z y z

x y x θθθθθθ??-??-???????Θ=?-?=-????????-??-??

?? []3310000.0060.004(1)()0100.00600.0020010.0040.0020C n C n I I ?-???????????+=+?Θ=+-????????????-??????

10.1 The frame XYZ rotates around its axis Z for an angle of 60 degrees. The unit vectors along

axes X, Y, Z are i, j, k respectively. Then the quaternion describing this rotation can written as

D. 坐标系绕Z 轴旋转60°，四元数表示为D A. 322i + B. 1322k + C. 1344i + D. 3122

k + 10.2 If q1, q2, and q3 are three normalized quaternions, then D. q1,q2,q3均为标准化四元数

A.1221q q q q =

B.123213()()q q q q q q =

C.***1212()q q q q =

D.1*11q q -=

10.3 A fixed vector V is coordinated as k V j V i V V z y x ++= in frame XYZ, and

as ''''''k V j V i V V z y x ++=in frame X’Y’Z’, where i, j, k and i’, j’, k’ the unit vectors of the frames XYZ and X’Y’Z’ respectively. The rotation from XYZ to X’Y’Z’ can be described by a quaternion q. Using imageries, the transformation from z y x V V V ,,to ''',,z y x V V V can be accomplished by q V q V εε1'-=, where '

εV is the imagery of V in the frame X’Y’Z’, and εV is the imagery of V in XYZ. Then D

A.'''e x y z V V i V j V k =++

B.'e x y z V V i V j V k =++

C.''''''e x y z V V i V j V k =++

D.''''e x y z V V i V j V k =++

10.4 (F) The body of a vehicle has made three successive rotations, described by quaternions q1,

q2 , and q3 respectively, in the order of rotation. If the rotating axes of q1, q2, q3 are all in imagery forms, then the combination of these rotations can be described by quaternion 321q q q q = .

(×)一个刚体做三次连转，分别用四元数q1q2q3表示，如果是映像方式合成，合成后的

转动四元数表示为321q q q q = 。 应为123q q q q =

10.5 The attitude of a vehicle is described by a quaternion q, and its angular rate by ω, then q can

be determined by solving the differential equation D. 四元数的微分方程

A. q q ω=

B. q q ω=

C. 12q q ω=

D. 12

q q ω= 10.6 A SINS is used in a vehicle. At time n , the axis X of the vehicle frame points to the east, Y is

60 degrees above the north. 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. 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. Solution: At time n , the axis X of the vehicle frame points to the east, Y is 60 degrees above the north. So rotation around axis E of geographical frame for 60 degrees produces the body frame at time n. 3/πθ= i n =

()[cos(/6)sin(/6)00]T q n ππ=

000.0020.040.0600.00200.0060.00400.0040.00600.00200.0060.0040.0020x y z x z y y z x z y x θθθθθθθθθθθθ-?-?-?---??????????-?-?????Θ==???-????-??????-?-????

?? 400.0020.0040.006cos(/6)0.00200.0060.004sin(/6)11(1)()0.0040.00600.0020220.0060.0040.00200q n I q n I ππ?---???????????-????????+=+?Θ=+????????-??????????-??????

14.1 (T) Increasing the size of a Sagnac interferometer is helpful to improving its sensitivity to

angular rate input.

(√)提高干涉仪的尺寸有利于提高它对角速度输入的灵敏度。

14.2 (F) Laser gyro is based on measurement of the optic path difference between two beams of

lasers propagating in opposite directions within a closed path.

(×)激光陀螺是基于测量在一个封闭回路中两束传播方向相反的激光的光程差。

14.3 (F) In a laser gyro, double anodes are employed to reduce the lock-in error caused by

Langmuir flow.

(×)在激光陀螺中，双阳极的应用时为了降低Langmuir 效应造成的自锁误差。零偏误差 15.1 (T) Phase biasing is adopted in a fiber optic gyro to improve its measurement sensitivity. (√)光纤陀螺为提高测量灵敏度采用了相位偏置。

15.2 Which of the following features is not counted as an advantage of a closed-loop FOG over an

open-loop one? D. 下列哪个特征不是闭环干涉型光纤陀螺特有的D 。

A. better linearity 线性度好

B. wider measurement range 测量范围广

C. higher accuracy 灵敏度高

D. smaller size 体积小

16.1 Here is a tuning fork gyro. The input angular rate and the instant(瞬时) vibrating velocities of

the terminal(端部) masses are as shown. Please use arrows to indicate the directions of the Coriolis accelerations k a of the masses, the Coriolis inertial forces c F , and the Coriolis inertial torque c T

16.2 In a hemispheric resonant gyro, an elastic mass ring in the resonator is vibrating with a

4-node pattern. Now the shape of the ring is changing from a circle (the solid curve) to an ellipse (the dotted curve). Suppose the base is rotating anti-clockwise around the central axis of the ring. Please mark with arrow the direction of vibrating velocity v and Coriolis inertial force k f of each node and anti-node, and the direction of the major axis L of the ellipse actually formed at the end of this deformation.

图 16.1 图16.2

ω

v

v ω