CN103231810A - Maneuvering unloading pitch axis angular momentum method by satellite pitching axis attitude - Google Patents

Abstract

The invention relates to the technical field of the spacecraft attitude control and provides a maneuvering unloading pitch axis angular momentum method by satellite pitching axis attitude. The maneuvering unloading the pitch axis angular momentum method by the satellite pitching axis attitude comprises step one, measuring and confirming the satellite pitch axis angular momentum hun-y needs to be unloaded; step two, confirming gravity gradient torque the satellite bears according to satellite rotational inertia; step three, estimating time tend needed by the maneuvering thetam of the satellite pitch axis and angular momentum humanu which is accumulated by the gravity gradient torque on the pitch axis in the maneuvering process; step four, solving an angle thetam the satellite needs to be maneuvered according to the hun-y and the humanu; step five, calculating time thold the angle thetam needs to be kept according to the hun-y, the humanu and the confirmed thetam in step four; and step six, confirming satellite rotational inertia distribution forms which guarantee that the satellite can perform maneuvering with enough angular momentum space. The maneuvering unloading the pitch axis angular momentum method by the satellite pitching axis attitude is applied to the technical field of the spacecraft attitude control and solves the problems that devices are utilized to unload in the prior art and the costs of unloading devices are high.

Description

A kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum

Technical field

The present invention relates to spacecraft attitude control technology field, be specifically related to utilize the motor-driven unloading pitch axis of satellite pitch axis rapid posture moment of momentum method.

Background technology

Satellite with fast reserve ability can be finished the motor-driven of wide-angle in a short period of time and can follow the tracks of target accurately.In order to satisfy the requirement of the motor-driven rapidity of satellite and particularity simultaneously, usually use momentum exchange device as actuating unit, simultaneously the actuating unit of the motor-driven rapidity requirement satellite of satellite has enough moment of momentum spaces, and therefore how conveniently the actuating unit of satellite being unloaded is a problem that is worth research.

The normal conditions satellite uses magnetic torquer or air jet system unloading, though magnetic torquer can provide continuous unloading moment in real time, but the unload forces moment ratio that magnetic torquer can provide is less, if satellite exists bigger disturbance torque to utilize magnetic torquer to unload and needs long time, the air jet system unloading can provide bigger unloading moment, but because the air jet system consume fuel life-span is limited, be not well suited for for long playing rocket, in addition, air jet system is also relatively expensive.

Summary of the invention

The present invention is the problem that will solve existing method operative installations unloading and discharging gear costliness, proposes a kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum.

A kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum, detailed process is as follows:

The pitch axis angular momentum h that satellite need unload is determined in step 1, measurement _{Un_y}, concrete steps are:

Measure the moment of momentum of each momentum exchange actuating unit at the component of body coordinate system, with i momentum exchange actuating unit moment of momentum at the representation in components of body coordinate system be Can obtain the total angular momentum of all momentum exchange actuating units thus at the component h of pitch axis _{Un_y}, expression formula is:

$h_{\mathrm{un}\_y}=-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{h}_i^b\·y_b^b=-h_c^b\·y_b^b=-h_c^{\mathrm{by}}---\left(1\right)$

In the formula, described body coordinate system is body coordinate system ox _b, y _bz _bOverlap with inertia principal axes system, initial point is at the barycenter of satellite, and each coordinate axle and satellite body are connected, body coordinate system ox _by _bz _bMiddle ox _bBe the axis of rolling, oy _bBe pitch axis, oz _bBe yaw axis, symbol b represents the amount relevant with body coordinate system;

Be 3 * 1 array, represent i momentum exchange actuating unit moment of momentum at the component of body coordinate system,

Represent the summation of all actuating unit moment of momentums at the component of body coordinate system,

Represent that the summation of all actuating unit moment of momentums is at the component of body coordinate system pitch axis, h _{Un_y}Be the pitch axis moment of momentum size of needs unloading, $y_b^b={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^T$ Be the pitch axis of the body coordinate system component in body coordinate system, n is the quantity of actuating unit, and i is the integer greater than 0;

Step 2, determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia: the body coordinate system of normal conditions satellite overlaps with principal axis of inertia system of axes, so the expression formula of gravity gradient torque can be expressed as:

In the formula, μ is the terrestrial gravitation constant, and R represents the distance of satellite barycenter and earth centroid,

Suffered three gravity gradient torques of expression satellite are at the component of body series, I _x, I _y, I _zRepresent the satellite axis of rolling, pitch axis, the corresponding principal moments of yaw axis respectively,

θ represents to change roll angle and the pitch angle that order is described by 3-2-1; Wherein, described 3-2-1 changes in the order 3 representatives around oz _bRotate, 2 representatives are around oy _bAxle rotates, and 1 representative is around ox _bRotate.

Step 3, the motor-driven θ of estimation satellite pitch axis _mNeeded time t _End, and the angular momentum h that gravity gradient torque accumulates at pitch axis in the mobile process _Manu

The motor-driven θ of satellite pitch axis _mThe used time can be expressed as:

t _end＝ω _ymax/a _ymax+θ _m/ω _ymax (3)

In the formula, t _EndBe the motor-driven θ of satellite pitch axis _mThe used time, ω _YmaxBe the maximum angular rate in the satellite pitch axis mobile process, a _YmaxMaximum angular acceleration in the satellite pitch axis mobile process;

Employing is got the method for mobile process gravity gradient torque aviation value and is estimated h _Manu, satellite is in the three axis stabilization state before the unloading, and three suffered gravity gradient torques are 0, motor-driven θ _mAfter the angle, only pitch axis is subjected to the gravity gradient torque effect, and expression formula is:

$T_G^{\mathrm{by}}=\frac{3\mathrm{\μ}}{{2R}^3}(I_z-I_x)\sin 2{\mathrm{\θ}}_m---\left(4\right)$

In the formula,

The expression gravity gradient torque is at the component of body series pitch axis;

Mean gravity gradient moment according to motor-driven front and back can be estimated the moment of momentum that accumulates in the mobile process, and expression formula is:

$h_{\mathrm{manu}}=\frac{1}{2}(0+\frac{3\mathrm{\μ}}{{2R}^3}(I_z-I_x)\sin 2{\mathrm{\θ}}_m)t_{\mathrm{end}}---\left(5\right)$

Step 4, according to h _{Un_y}With h _ManuFind the solution satellite and need motor-driven angle θ _m

Step 5, according to h _{Un_y}, h _ManuWith the determined θ of step 4 _m, calculate the time t that needs to keep this angle _Hold:

Need after the unloading motor-drivenly to be the three axis stabilization state because satellite is finished, so satellite is keeping θ _mThe moment of momentum that accumulates during motion should satisfy relation

$\frac{3\mathrm{\μ}}{{2R}^3}(I_z-I_x)\sin 2{\mathrm{\θ}}_m\·t_{\mathrm{hold}}=h_{\mathrm{un}\_y}-{2h}_{\mathrm{manu}}---\left(6\right)$

Therefore can solve satellite and keep θ _mTime t _HoldFor:

$t_{\mathrm{hold}}=\frac{{2R}^3(h_{\mathrm{un}\_y}-2h_{\mathrm{manu}})}{3\mathrm{\μ}(I_z-I_x)\sin 2{\mathrm{\θ}}_m}---\left(7\right)$

Step 6, determine to guarantee that satellite has enough moment of momentums space to carry out motor-driven satellite rotor inertia distribution form:

Its relational expression that specifically needs to satisfy is:

I _z□I _x (8)

In the formula, symbol represents I _xBe far longer than I _z

Effect of the present invention:

(1) do not need to use other pitch axis discharging gears, only pass through the motor-driven of pitch axis, can unload the moment that pitch axis accumulates, saved cost and the space of satellite;

(2) discharging method simple possible, and have certain precision, be fit to the actual satellite application with fast reserve ability;

(3) provided the inertia distribution form that uses the satellite that this method unloads the pitch axis moment of momentum, actual satellite can be in conjunction with the unloading strategy design satellite task of pitch axis and the distribution of inertia, the realization task and unload between balance.

Description of drawings

Fig. 1 is diagram of circuit of the present invention;

Fig. 2 is satellite mobile process scheme drawing;

Fig. 3 is the change curve of attitude angle in the satellite pitch axis uninstall process; Among the figure

Represent the roll angle curve,----among the figure-represent the pitch angle curve, among the figure

Represent the yaw angle curve;

Fig. 4 is satellite pitch axis uninstall process three shaft angle momentum change curves; Among the figure

Represent axis of rolling moment of momentum change curve,----among the figure-represent pitch axis moment of momentum change curve, among the figure

Represent yaw axis moment of momentum change curve;

Fig. 5 is satellite pitch axis uninstall process three shaft angle momentum change partial enlarged drawings; Among the figure

Represent axis of rolling moment of momentum change curve,----among the figure-represent pitch axis moment of momentum change curve, among the figure

Represent yaw axis moment of momentum change curve.

The specific embodiment

The specific embodiment one: present embodiment is described in conjunction with Fig. 1～Fig. 5: a kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum, detailed process is as follows:

The pitch axis angular momentum h that satellite need unload is determined in step 1, measurement _{Un_y}, concrete steps are:

Measure the moment of momentum of each momentum exchange actuating unit at the component of body coordinate system, with i momentum exchange actuating unit moment of momentum at the representation in components of body coordinate system be

Can obtain the total angular momentum of all momentum exchange actuating units thus at the component h of pitch axis _{Un_y}, expression formula is:

$h_{\mathrm{un}\_y}=-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{h}_i^b\·y_b^b=-h_c^b\·y_b^b=-h_c^{\mathrm{by}}---\left(9\right)$

In the formula, described body coordinate system is body coordinate system ox _by _bz _bOverlap with inertia principal axes system, initial point is at the barycenter of satellite, and each coordinate axle and satellite body are connected, body coordinate system ox _by _bz _bMiddle ox _bBe the axis of rolling, oy _bBe pitch axis, oz _bBe yaw axis, symbol b represents the amount relevant with body coordinate system;

Be 3 * 1 array, represent i momentum exchange actuating unit moment of momentum at the component of body coordinate system,

Represent the summation of all actuating unit moment of momentums at the component of body coordinate system,

Represent that the summation of all actuating unit moment of momentums is at the component of body coordinate system pitch axis, h _{Un_y}Be the pitch axis moment of momentum size of needs unloading, $y_b^b={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^T$ Be the pitch axis of the body coordinate system component in body coordinate system, n is the quantity of actuating unit, and i is the integer greater than 0;

Step 2, determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia: the body coordinate system of normal conditions satellite overlaps with principal axis of inertia system of axes, so the expression formula of gravity gradient torque can be expressed as:

In the formula, μ is the terrestrial gravitation constant, and R represents the distance of satellite barycenter and earth centroid,

Suffered three gravity gradient torques of expression satellite are at the component of body series, I _x, I _y, I _zRepresent the satellite axis of rolling, pitch axis, the corresponding principal moments of yaw axis respectively,

θ represents to change roll angle and the pitch angle that order is described by 3-2-1; Wherein, described 3-2-1 changes in the order 3 representatives around oz _bRotate, 2 representatives are around oy _bAxle rotates, and 1 representative is around ox _bRotate.

Step 3, the motor-driven θ of estimation satellite pitch axis _mNeeded time t _End, and the angular momentum h that gravity gradient torque accumulates at pitch axis in the mobile process _Manu

The motor-driven θ of satellite pitch axis _mThe used time can be expressed as:

t _end＝ω _ymax/a _ymax+θ _m/ω _xmax(11)

In the formula, t _EndBe the motor-driven θ of satellite pitch axis _mThe used time, ω _YmaxBe the maximum angular rate in the satellite pitch axis mobile process, a _YmaxMaximum angular acceleration in the satellite pitch axis mobile process;

Employing is got the method for mobile process gravity gradient torque aviation value and is estimated h _Manu, satellite is in the three axis stabilization state before the unloading, and three suffered gravity gradient torques are 0, motor-driven θ _mAfter the angle, only pitch axis is subjected to the gravity gradient torque effect, and expression formula is:

$T_G^{\mathrm{by}}=\frac{3\mathrm{\μ}}{{2R}^3}(I_z-I_x)\sin 2{\mathrm{\θ}}_m---\left(12\right)$

In the formula,

The expression gravity gradient torque is at the component of body series pitch axis;

Mean gravity gradient moment according to motor-driven front and back can be estimated the moment of momentum that accumulates in the mobile process, and expression formula is:

$h_{\mathrm{manu}}=\frac{1}{2}(0+\frac{3\mathrm{\μ}}{{2R}^3}(I_z-I_x)\sin 2{\mathrm{\θ}}_m)t_{\mathrm{end}}---\left(13\right)$

Step 4, according to h _{Un_y}With h _ManuFind the solution satellite and need motor-driven angle θ _m

Step 5, according to h _{Un_y}, h _ManuWith the determined θ of step 4 _m, calculate the time t that needs to keep this angle _Hold:

Need after the unloading motor-drivenly to be the three axis stabilization state because satellite is finished, so satellite is keeping θ _mThe moment of momentum that accumulates during motion should satisfy relation

$\frac{3\mathrm{\μ}}{{2R}^3}(I_z-I_x)\sin 2{\mathrm{\θ}}_m\·t_{\mathrm{hold}}=h_{\mathrm{un}\_y}-{2h}_{\mathrm{manu}}---\left(14\right)$

Therefore can solve satellite and keep θ _mTime t _HoldFor:

$t_{\mathrm{hold}}=\frac{{2R}^3(h_{\mathrm{un}\_y}-2h_{\mathrm{manu}})}{3\mathrm{\μ}(I_z-I_x)\sin 2{\mathrm{\θ}}_m}---\left(15\right)$

Step 6, determine to guarantee that satellite has enough moment of momentums space to carry out motor-driven satellite rotor inertia distribution form:

Its relational expression that specifically needs to satisfy is:

I _z□I _z (16)

In the formula, symbol represents I _xBe far longer than I _z

In the present embodiment, the satellite rotor inertia: $I=\left[\begin{array}{ccc}4000& 0& 0\\ 0& 4000& 0\\ 0& 0& 1000\end{array}\right]\mathrm{kg}\·m^2,$ The maximum output torque of pitch axis actuating unit is 0.4Nm, and the lock angle momentum is 50Nms;

Initial parameter: the satellite initial attitude is Φ ₀=[0 0 0] °, the initial angular momentum of actuating unit is h _C0=[0 45 0] Nms, satellite moves at circular orbit, and orbit angular velocity is 0.00107rad/s;

h _{Un_y}=-45Nm, because | h _{Un_y}|＞| 2h _Manu(45 °) |, so satellite needs motor-driven pitching angle theta _m=45 °, according to the ability of actuating unit, getting maximum motor-driven cireular frequency is ω _Ymax=0.005rad/s estimates that the motor-driven used time of satellite is t _End=207s, the moment of momentum that accumulates in the estimation satellite mobile process is h _Manu=1.068Nms, can calculate satellite needs θ _mTime be t _Hold=8517s;

Unloading strategy begins unloading for 200s, and satellite is motor-driven to arrive θ=45 °, at 200s+207s+t _HoldThe start of evolution of=8924s satellite is ° motor-driven to θ=0 ° by θ=45, finishes unloading.This example is used Matlab/Simulink software, adopts the ODE4 algorithm, simulation step length 0.1s.

The present embodiment effect:

(1) do not need to use other pitch axis discharging gears, only pass through the motor-driven of pitch axis, can unload the moment that pitch axis accumulates, saved cost and the space of satellite;

(2) discharging method simple possible, and have certain precision, be fit to the actual satellite application with fast reserve ability;

(3) provided the inertia distribution form that uses the satellite that this method unloads the pitch axis moment of momentum, actual satellite can be in conjunction with the unloading strategy design satellite task of pitch axis and the distribution of inertia, the realization task and unload between balance.

The specific embodiment two: what present embodiment and the specific embodiment one were different is: find the solution the motor-driven required time t of satellite in the step 3 _EndDetailed process be:

Step 3 one: the motor-driven form of satellite is: beginning is with the maximum torque accelerated movement, when the satellite rotating speed reaches ω _YmaxAfter stop satellite being applied moment, allow satellite with ω _YmaxCireular frequency carries out normal speed and rolls, and at last the maximum torque of satellite time direction is slowed down, and guarantee that the satellite attitude angle reaches designated value, and attitude angular velocity is 0;

Step 3 two: according to the motor-driven form of satellite, maximum motor-driven angular velocity omega _YmaxAnd the angular acceleration a of satellite maximum _Ymax, the used time of satellite accelerating sections and accelerating sections that can estimate is

t ₁＝t _end-t ₂＝ω _ymax/a _ymax (17)

In the formula, t ₁Be used time of satellite accelerating sections, t ₂The time that reduces speed now for satellite;

Step 3 three: the area that Satellite Angle speed and coordinate axle surround equals motor-driven attitude angle θ _mThereby, can obtain expression formula

t ₂＝θ _m/ω _ymax (18)

At last, can get expression formula by formula (17) and formula (18)

t _end＝ω _ymax/a _ymax+θ _m/ω _ymax (19)

Other step and parameter are identical with the specific embodiment one.

The specific embodiment three: what present embodiment was different with the specific embodiment one or two is: the detailed process of step 4 is:

Step 4 one: make the amplitude of gravity gradient torque get maxim, i.e. θ _m=45 °, calculate satellite by 0 ° of motor-driven angular momentum h that accumulates in 45 ° the process _Manu(45 °), satellite is identical by the moment of momentum that accumulates in 45 ° of motor-driven processes of 0 ° with satellite by the moment of momentum that accumulates in 0 ° of motor-driven process of 45 °, therefore, as motor-driven angle θ _mUnder=45 ° the prerequisite, the moment of momentum summation that accumulates in the satellite mobile process is 2h _Manu(45 °);

Step 4 two: relatively | 2h _Manu(45 °) | with | h _{Un_y}| size:

If | h _{Un_y}| 〉=| 2h _Manu(45 °) | then get θ _m=45 °;

If | h _{Un_y}|＜| 2h _Manu(45 °) |, θ then _mShould satisfy equation:

$h_{\mathrm{un}\_y}={2h}_{\mathrm{manu}}\left({\mathrm{\θ}}_m\right)=\frac{3\mathrm{\μ}}{{2R}^3}(I_z-I_x)\sin 2{\mathrm{\θ}}_m{t}_{\mathrm{end}}\left({\mathrm{\θ}}_m\right)---\left(20\right)$

In the formula, h _Manu(θ _m) and t _End(θ _m) expression h _ManuWith t _EndBe θ _mFunction, the nonlinear equation of finding the solution formula (20) namely can solve required motor-driven angle θ _m, satellite does not keep θ in this case _mProcess, only be motor-driven to θ by 0 ° fast _m, motor-driven to 0 ° more at once, finish unloading.Other step and parameter are identical with the specific embodiment one or two.

The specific embodiment four: what present embodiment was different with one of specific embodiment one to three is: the concrete solution procedure of the distribution mode of the described satellite rotor inertia of step 6 is:

Can utilize satellite pitch axis attitude maneuver unloading pitch axis moment of momentum, need the inertia distribution of satellite to satisfy condition:

(1) satellite can provide enough big gravity gradient torque, therefore need satisfy condition | I _z-I _x| 0;

(2) to have enough moment of momentum spaces to carry out motor-driven for satellite, and namely pitch axis motor-driven do not need actuating unit to the saturated direction motion of moment of momentum:

Make a concrete analysis of as follows: if satellite pitch axis actuating unit has moment of momentum at pitch axis

And near saturation value, need the angular momentum h of unloading this moment _{Un_y}＜0, this moment, satellite can only provide moment

(moment of momentum that guarantees the mobile process actuating unit does not increase), this moment, satellite can only be motor-driven to θ _m＞0, in order to guarantee t _Hold＞0, need to guarantee I according to formula (7) _z＜I _xIf in like manner

Can shift onto out equally and need satisfy I _z＜I _x

Comprehensively (1) and (2) can obtain being applicable to the distribution of the satellite rotor inertia of the motor-driven unloading pitch axis of pitch axis moment of momentum the I that should satisfy condition _zI _xOther step and parameter are identical with one of specific embodiment one to three.

Claims (4)

1. method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum is characterized in that detailed process is as follows:

The pitch axis angular momentum h that satellite need unload is determined in step 1, measurement _{Un_y}, concrete steps are:

Measure the moment of momentum of each momentum exchange actuating unit at the component of body coordinate system, with i momentum exchange actuating unit moment of momentum at the representation in components of body coordinate system be Can obtain the total angular momentum of all momentum exchange actuating units thus at the component h of pitch axis _{Un_y}, expression formula is:

In the formula, described body coordinate system is body coordinate system ox _by _bz _bOverlap with inertia principal axes system, initial point is at the barycenter of satellite, and each coordinate axle and satellite body are connected, body coordinate system ox _by _bz _bMiddle ox _bBe the axis of rolling, oy _bBe pitch axis, oz _bBe yaw axis, symbol b represents the amount relevant with body coordinate system;

Be 3 * 1 array, represent i momentum exchange actuating unit moment of momentum at the component of body coordinate system,

Represent the summation of all actuating unit moment of momentums at the component of body coordinate system,

Represent that the summation of all actuating unit moment of momentums is at the component of body coordinate system pitch axis, h _{Un_y}Be the pitch axis moment of momentum size of needs unloading,

Be the pitch axis of the body coordinate system component in body coordinate system, n is the quantity of actuating unit, and i is the integer greater than 0;

Step 2, determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia: the body coordinate system of normal conditions satellite overlaps with principal axis of inertia system of axes, so the expression formula of gravity gradient torque can be expressed as:

In the formula, μ is the terrestrial gravitation constant, and R represents the distance of satellite barycenter and earth centroid,

Suffered three gravity gradient torques of expression satellite are at the component of body series, I _x, I _y, I _zRepresent the satellite axis of rolling, pitch axis, the corresponding principal moments of yaw axis respectively,

θ represents to change roll angle and the pitch angle that order is described by 3-2-1; Wherein, described 3-2-1 changes in the order 3 representatives around oz _bRotate, 2 representatives are around oy _bAxle rotates, and 1 representative is around ox _bRotate.

Step 3, the motor-driven θ of estimation satellite pitch axis _mNeeded time t _End, and the angular momentum h that gravity gradient torque accumulates at pitch axis in the mobile process _Manu

The motor-driven θ of satellite pitch axis _mThe used time can be expressed as:

t _end＝ω _ymax/a _ymax+θ _m/ω _ymax (3)

In the formula, t _EndBe the motor-driven θ of satellite pitch axis _mThe used time, ω _YmaxBe the maximum angular rate in the satellite pitch axis mobile process, a _YmaxMaximum angular acceleration in the satellite pitch axis mobile process;

Employing is got the method for mobile process gravity gradient torque aviation value and is estimated h _Manu, satellite is in the three axis stabilization state before the unloading, and three suffered gravity gradient torques are 0, motor-driven θ _mAfter the angle, only pitch axis is subjected to the gravity gradient torque effect, and expression formula is:

In the formula,

The expression gravity gradient torque is at the component of body series pitch axis;

Mean gravity gradient moment according to motor-driven front and back can be estimated the moment of momentum that accumulates in the mobile process, and expression formula is:

Step 4, according to h _{Un_y}With h _ManuFind the solution satellite and need motor-driven angle θ _m

Step 5, according to h _{Un_y}, h _ManuWith the determined θ of step 4 _m, calculate the time t that needs to keep this angle _Hold:

Need after the unloading motor-drivenly to be the three axis stabilization state because satellite is finished, so satellite is keeping θ _mThe moment of momentum that accumulates during motion should satisfy relation

Therefore can solve satellite and keep θ _mTime t _HoldFor:

Step 6, determine to guarantee that satellite has enough moment of momentums space to carry out motor-driven satellite rotor inertia distribution form:

Its relational expression that specifically needs to satisfy is:

I _z□I _x (8)

In the formula, symbol represents I _xBe far longer than I _z

2. a kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum according to claim 1 is characterized in that finding the solution in the step 3 the motor-driven required time t of satellite _EndDetailed process be:

Step 3 one: the motor-driven form of satellite is: beginning is with the maximum torque accelerated movement, when the satellite rotating speed reaches ω _YmaxAfter stop satellite being applied moment, allow satellite with ω _YmaxCireular frequency carries out normal speed and rolls, and at last the maximum torque of satellite time direction is slowed down, and guarantee that the satellite attitude angle reaches designated value, and attitude angular velocity is 0;

Step 3 two: according to the motor-driven form of satellite, maximum motor-driven angular velocity omega _YmaxAnd the angular acceleration a of satellite maximum _Ymax, the used time of satellite accelerating sections and accelerating sections that can estimate is

t ₁＝t _end-t ₂＝ω _ymax/a _ymax (9)

In the formula, t ₁Be used time of satellite accelerating sections, t ₂The time that reduces speed now for satellite;

Step 3 three: the area that Satellite Angle speed and coordinate axle surround equals motor-driven attitude angle θ _mThereby, can obtain expression formula

t ₂＝θ _m/ω _ymax (10)

At last, can get expression formula by formula (9) and formula (10)

t _end＝ω _ymax/a _ymax+θ _m/ω _ymax (11)。

3. a kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum according to claim 1 is characterized in that the detailed process of step 4 is:

Step 4 one: make the amplitude of gravity gradient torque get maxim, i.e. θ _m=45 °, calculate satellite by 0 ° of motor-driven angular momentum h that accumulates in 45 ° the process _Manu(45 °), satellite is identical by the moment of momentum that accumulates in 45 ° of motor-driven processes of 0 ° with satellite by the moment of momentum that accumulates in 0 ° of motor-driven process of 45 °, therefore, as motor-driven angle θ _mUnder=45 ° the prerequisite, the moment of momentum summation that accumulates in the satellite mobile process is 2h _Manu(45 °);

Step 4 two: relatively | 2h _Manu(45 °) | with | h _{Un_y}| size:

If | h _{Un_y}| 〉=| 2h _Manu(45 °) | then get θ _m=45 °;

If | h _{Un_y}|＜| 2h _Manu(45 °) |, θ then _mShould satisfy equation:

In the formula, h _Manu(θ _m) and t _End(θ _m) expression h _ManuWith t _EndBe θ _mFunction, the nonlinear equation of finding the solution formula (12) namely can solve required motor-driven angle θ _m, satellite does not keep θ in this case _mProcess, only be motor-driven to θ by 0 ° fast _m, motor-driven to 0 ° more at once, finish unloading.

4. a kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum according to claim 1 is characterized in that the concrete solution procedure of the distribution form of the described satellite rotor inertia of step 6 is:

Can utilize satellite pitch axis attitude maneuver unloading pitch axis moment of momentum, need the inertia distribution of satellite to satisfy condition:

(1) satellite can provide enough big gravity gradient torque, therefore need satisfy condition | I _z-I _x| 0;

(2) to have enough moment of momentum spaces to carry out motor-driven for satellite, and namely pitch axis motor-driven do not need actuating unit to the saturated direction motion of moment of momentum:

Make a concrete analysis of as follows: if satellite pitch axis actuating unit has moment of momentum at pitch axis

And near saturation value, need the angular momentum h of unloading this moment _{Un_y}＜0, this moment, satellite can only provide moment

(moment of momentum that guarantees the mobile process actuating unit does not increase), this moment, satellite can only be motor-driven to θ _m＞0, in order to guarantee t _Hold＞0, need to guarantee I according to formula (7) _z＜I _xIf in like manner

Can shift onto out equally and need satisfy I _z＜I _x

Comprehensively (1) and (2) can obtain being applicable to the distribution of the satellite rotor inertia of the motor-driven unloading pitch axis of pitch axis moment of momentum the I that should satisfy condition _zI _x

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