CN103231810B - 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 utilizing satellite pitch axis attitude maneuver to unload pitch axis moment of momentum

Technical field

The present invention relates to technical field of spacecraft attitude control, be specifically related to utilize satellite pitch axis rapid attitude maneuver to unload pitch axis moment of momentum method.

Background technology

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

Normal conditions satellite uses magnetic torquer or air jet system unloading, although magnetic torquer can provide continuous print to unload moment in real time, but the unloading force square that magnetic torquer can provide is smaller, if the larger disturbance torque of satellite existence utilizes magnetic torquer to carry out unloading need long time, air jet system unloading can provide larger unloading moment, but due to air jet system consume fuel restricted lifetime, long playing rocket is not well suited for, in addition, air jet system is also relatively expensive.

Summary of the invention

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

Utilize satellite pitch axis attitude maneuver to unload a method for pitch axis moment of momentum, detailed process is as follows:

Step one, measurement determine that satellite needs the pitch axis angular momentum h of unloading _{un_y}, concrete steps are:

Measure the component of moment of momentum in body coordinate system of each momentum exchange actuating unit, by i-th momentum exchange actuating unit moment of momentum at the representation in components of body coordinate system be the component h of total angular momentum at pitch axis of all momentum exchange actuating units can be obtained thus _{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 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 _bfor the axis of rolling, oy _bfor pitch axis, oz _bfor yaw axis, symbol b represents the amount relevant with body coordinate system;

be the array of 3 × 1, represent the component of i-th momentum exchange actuating unit moment of momentum in body coordinate system, represent the component of summation in body coordinate system of all actuating unit moment of momentums, represent the component of summation at body coordinate system pitch axis of all actuating unit moment of momentums, h _{un_y}for needing the pitch axis moment of momentum size of unloading, $y_b^b={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^T$ For the pitch axis of body coordinate system is at the component of body coordinate system, n is the quantity of actuating unit, i be greater than 0 integer;

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

In formula, μ is Gravitational coefficient of the Earth, and R represents the distance of centroid of satellite and earth centroid, represent that suffered by satellite, three axle gravity gradient torques are at the component of body series, I _x, I _y, I _zrepresent the satellite axis of rolling, pitch axis, principal moments corresponding to yaw axis respectively, θ represents the roll angle and the pitch angle that turn sequence description by 3-2-1; Wherein, described 3-2-1 to turn in sequence 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 _mrequired time t _end, and the angular momentum h that in mobile process, gravity gradient torque accumulates at pitch axis _manu;

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

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

In formula, t _endfor the motor-driven θ of satellite pitch axis _mtime used, ω _ymaxfor the maximum angular rate in satellite pitch axis mobile process, a _ymaxmaximum angular acceleration in satellite pitch axis mobile process;

The method of getting mobile process gravity gradient torque aviation value is adopted to estimate h _manu, before unloading, satellite is in three axis stabilization state, and suffered by three axles, gravity gradient torque is 0, motor-driven θ _mafter angle, only pitch axis is subject to 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 formula, represent the component of gravity gradient torque at body series pitch axis;

Mean gravity gradient moment according to motor-driven front and back can estimate the moment of momentum accumulated in 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 _manusolve satellite and need motor-driven angle θ _m;

Step 5, according to h _{un_y}, h _manuθ determined with step 4 _m, calculate and need the time t keeping this angle _hold:

Due to satellite complete unloading after need motor-driven for three axis stabilization state, therefore satellite is at maintenance θ _mthe moment of momentum accumulated during motion should meet 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 ensure that satellite has enough moment of momentum spaces to carry out motor-driven satellite rotor inertia distribution form:

The relational expression of its concrete demand fulfillment is:

I _z□I _x(8)

In 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, motor-driven by means of only pitch axis, the moment that pitch axis accumulates can be unloaded, save cost and the space of satellite;

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

(3) give and use this method to the inertia distribution form of the satellite that pitch axis moment of momentum unloads, actual satellite can in conjunction with the distribution of the unloading Strategy Design satellite task of pitch axis with inertia, realizes task and balance between unloading.

Accompanying drawing explanation

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

Fig. 2 is the motor-driven process schematic of satellite;

Fig. 3 is the change curve of attitude angle in satellite pitch axis uninstall process; In figure -----represents pitch angle curve to represent roll angle curve, in figure, in figure represent yaw angle curve;

Fig. 4 is satellite pitch axis uninstall process three shaft angle momentum change curve; In figure represent axis of rolling moment of momentum change curve, in figure,-----represents pitch axis moment of momentum change curve, in figure represent yaw axis moment of momentum change curve;

Fig. 5 is satellite pitch axis uninstall process three shaft angle momentum change partial enlarged drawing; In figure represent axis of rolling moment of momentum change curve, in figure,-----represents pitch axis moment of momentum change curve, in figure represent yaw axis moment of momentum change curve.

Detailed description of the invention

Detailed description of the invention one: composition graphs 1 ~ Fig. 5 illustrates present embodiment: a kind of method utilizing satellite pitch axis attitude maneuver to unload pitch axis moment of momentum, detailed process is as follows:

Step one, measurement determine that satellite needs the pitch axis angular momentum h of unloading _{un_y}, concrete steps are:

Measure the component of moment of momentum in body coordinate system of each momentum exchange actuating unit, by i-th momentum exchange actuating unit moment of momentum at the representation in components of body coordinate system be the component h of total angular momentum at pitch axis of all momentum exchange actuating units can be obtained thus _{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 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 _bfor the axis of rolling, oy _bfor pitch axis, oz _bfor yaw axis, symbol b represents the amount relevant with body coordinate system;

be the array of 3 × 1, represent the component of i-th momentum exchange actuating unit moment of momentum in body coordinate system, represent the component of summation in body coordinate system of all actuating unit moment of momentums, represent the component of summation at body coordinate system pitch axis of all actuating unit moment of momentums, h _{un_y}for needing the pitch axis moment of momentum size of unloading, $y_b^b={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^T$ For the pitch axis of body coordinate system is at the component of body coordinate system, n is the quantity of actuating unit, i be greater than 0 integer;

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

In formula, μ is Gravitational coefficient of the Earth, and R represents the distance of centroid of satellite and earth centroid, represent that suffered by satellite, three axle gravity gradient torques are at the component of body series, I _x, I _y, I _zrepresent the satellite axis of rolling, pitch axis, principal moments corresponding to yaw axis respectively, θ represents the roll angle and the pitch angle that turn sequence description by 3-2-1; Wherein, described 3-2-1 to turn in sequence 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 _mrequired time t _end, and the angular momentum h that in mobile process, gravity gradient torque accumulates at pitch axis _manu;

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

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

In formula, t _endfor the motor-driven θ of satellite pitch axis _mtime used, ω _ymaxfor the maximum angular rate in satellite pitch axis mobile process, a _ymaxmaximum angular acceleration in satellite pitch axis mobile process;

The method of getting mobile process gravity gradient torque aviation value is adopted to estimate h _manu, before unloading, satellite is in three axis stabilization state, and suffered by three axles, gravity gradient torque is 0, motor-driven θ _mafter angle, only pitch axis is subject to 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 formula, represent the component of gravity gradient torque at body series pitch axis;

Mean gravity gradient moment according to motor-driven front and back can estimate the moment of momentum accumulated in 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 _manusolve satellite and need motor-driven angle θ _m;

Step 5, according to h _{un_y}, h _manuθ determined with step 4 _m, calculate and need the time t keeping this angle _hold:

Due to satellite complete unloading after need motor-driven for three axis stabilization state, therefore satellite is at maintenance θ _mthe moment of momentum accumulated during motion should meet 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 ensure that satellite has enough moment of momentum spaces to carry out motor-driven satellite rotor inertia distribution form:

The relational expression of its concrete demand fulfillment is:

I _z□I _z(16)

In formula, symbol represents I _xbe far longer than I _z.

In present embodiment, 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 lock angle momentum is 50Nms;

Initial parameter: satellite initial attitude is Φ ₀=[0 0 0] °, the initial angular momentum of actuating unit is h _c0=[0 45 0] Nms, satellite runs on circular orbit, and orbit angular velocity is 0.00107rad/s;

H _{un_y}=-45Nm, due to | h _{un_y}| > | 2h _manu(45 °) |, therefore 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 satellite motor-driven time used is t _end=207s, the moment of momentum accumulated in estimation satellite mobile process is h _manu=1.068Nms, can calculate satellite needs θ _mtime be t _hold=8517s;

Unloading strategy for 200s start unloading, satellite motor-driven arrives θ=45 °, at 200s+207s+t _holdthe start of evolution of=8924s satellite is ° motor-driven to θ=0 ° by θ=45, completes unloading.This example application Matlab/Simulink software, adopts ODE4 algorithm, simulation step length 0.1s.

Present embodiment effect:

(1) do not need to use other pitch axis discharging gears, motor-driven by means of only pitch axis, the moment that pitch axis accumulates can be unloaded, save cost and the space of satellite;

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

(3) give and use this method to the inertia distribution form of the satellite that pitch axis moment of momentum unloads, actual satellite can in conjunction with the distribution of the unloading Strategy Design satellite task of pitch axis with inertia, realizes task and balance between unloading.

Detailed description of the invention two: present embodiment and detailed description of the invention one unlike: solve the motor-driven required time t of satellite in step 3 _enddetailed process be:

Step 3 one: the motor-driven form of satellite is: start with maximum torque accelerated movement, when satellite rotating speed reaches ω _ymaxrear stopping applies moment to satellite, allows satellite with ω _ymaxcireular frequency carries out constant speed rolling, finally slows down to the maximum torque in satellite time direction, ensure that satellite attitude angle reaches designated value, and attitude angular velocity is 0;

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

t ₁＝t _end-t ₂＝ω _ymax/a _ymax(17)

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

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

t ₂＝θ _m/ω _ymax(18)

Finally, expression formula can be obtained by formula (17) and formula (18)

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

Other step and parameter identical with detailed description of the invention one.

Detailed description of the invention three: present embodiment and detailed description of the invention one or two unlike: 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 accumulated in the process of 45 ° _manu(45 °), satellite is identical by the moment of momentum accumulated in 45 ° of motor-driven processes of 0 ° with satellite by the moment of momentum accumulated in 0 ° of motor-driven process of 45 °, therefore, as motor-driven angle θ _munder the prerequisite of=45 °, the moment of momentum summation accumulated in satellite mobile process is 2h _manu(45 °);

Step 4 two: compare | 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 °) |, then θ _mshould equation be met:

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

In formula, h _manu(θ _m) and t _end(θ _m) represent h _manuwith t _endθ _mfunction, the nonlinear equation solving formula (20) namely can solve required motor-driven angle θ _m, satellite does not keep θ in this case _mprocess, be only fast motor-driven to θ by 0 ° _m, motor-driven to 0 ° more at once, complete unloading.Other step and parameter identical with detailed description of the invention one or two.

Detailed description of the invention four: one of present embodiment and detailed description of the invention one to three unlike: the concrete solution procedure of the distribution mode of satellite rotor inertia described in step 6 is:

Satellite pitch axis attitude maneuver can be utilized to unload pitch axis moment of momentum, need the inertia of satellite to distribute and satisfy condition:

(1) satellite can provide enough large gravity gradient torque, therefore demand fulfillment condition | I _z-I _x| 0;

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

Make a concrete analysis of as follows: if satellite pitch axis actuating unit has moment of momentum at pitch axis and close to saturation value, now need the angular momentum h unloaded _{un_y}< 0, now satellite can only provide moment (ensureing that the moment of momentum of mobile process actuating unit does not increase), now satellite can only be motor-driven to θ _m> 0, in order to ensure t _hold> 0, needs to ensure I according to formula (7) _z< I _x; If in like manner demand fulfillment I can be shifted out equally onto _z< I _x;

The distribution that comprehensively (1) and (2) can obtain the satellite rotor inertia being applicable to pitch axis motor-driven unloading pitch axis moment of momentum should satisfy condition I _zi _x.Other step and parameter identical with one of detailed description of the invention one to three.

Claims (4)

1. utilize satellite pitch axis attitude maneuver to unload a method for pitch axis moment of momentum, it is characterized in that detailed process is as follows:

Step one, measurement determine that satellite needs the pitch axis angular momentum h of unloading _{un_y}, concrete steps are:

Measure the component of moment of momentum in body coordinate system of each momentum exchange actuating unit, by i-th momentum exchange actuating unit moment of momentum at the representation in components of body coordinate system be the component h of total angular momentum at pitch axis of all momentum exchange actuating units can be obtained thus _{un_y}, expression formula is:

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

In 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 _bfor the axis of rolling, oy _bfor pitch axis, oz _bfor yaw axis, symbol b represents the amount relevant with body coordinate system;

be the array of 3 × 1, represent the component of i-th momentum exchange actuating unit moment of momentum in body coordinate system, represent the component of summation in body coordinate system of all actuating unit moment of momentums, represent the component of summation at body coordinate system pitch axis of all actuating unit moment of momentums, h _{un_y}for needing the pitch axis moment of momentum size of unloading, $y_b^b={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^T$ For the pitch axis of body coordinate system is at the component of body coordinate system, n is the quantity of actuating unit, i be greater than 0 integer;

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

In formula, μ is Gravitational coefficient of the Earth, and R represents the distance of centroid of satellite and earth centroid, represent that suffered by satellite, three axle gravity gradient torques are at the component of body series, I _x, I _y, I _zrepresent the satellite axis of rolling, pitch axis, principal moments corresponding to yaw axis respectively, θ represents the roll angle and the pitch angle that turn sequence description by 3-2-1; Wherein, described 3-2-1 to turn in sequence 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 _mrequired time t _end, and the angular momentum h that in mobile process, gravity gradient torque accumulates at pitch axis _manu;

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

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

In formula, t _endfor the motor-driven θ of satellite pitch axis _mtime used, ω _ymaxfor the maximum angular rate in satellite pitch axis mobile process, a _ymaxmaximum angular acceleration in satellite pitch axis mobile process;

The method of getting mobile process gravity gradient torque aviation value is adopted to estimate h _manu, before unloading, satellite is in three axis stabilization state, and suffered by three axles, gravity gradient torque is 0, motor-driven θ _mafter angle, only pitch axis is subject to gravity gradient torque effect, and expression formula is:

$T_G^{\mathrm{by}}=\frac{3\mathrm{\&mu;}}{2R^3}(I_z-I_x)\sin 2{\mathrm{\&theta;}}_m---\left(4\right)$

In formula, represent the component of gravity gradient torque at body series pitch axis;

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

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

Step 4, according to h _{un_y}with h _manusolve satellite and need motor-driven angle θ _m;

Step 5, according to h _{un_y}, h _manuθ determined with step 4 _m, calculate and need the time t keeping this angle _hold:

Due to satellite complete unloading after need motor-driven for three axis stabilization state, therefore satellite is at maintenance θ _mthe moment of momentum accumulated during motion should meet relation

$\frac{3\mathrm{\&mu;}}{2R^3}(I_z-I_x)\sin 2{\mathrm{\&theta;}}_m\&CenterDot;t_{\mathrm{hold}}=h_{\mathrm{un}\_y}-2h_{\mathrm{manu}}---\left(6\right)$

Therefore can solve satellite and keep θ _mtime t _holdfor:

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

Step 6, determine to ensure that satellite has enough moment of momentum spaces to carry out motor-driven satellite rotor inertia distribution form:

The relational expression of its concrete demand fulfillment is:

I _z＜＜I _x(8)

In formula, symbol < < represents I _xbe far longer than I _z.

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

Step 3 one: the motor-driven form of satellite is: start with maximum torque accelerated movement, when satellite rotating speed reaches ω _ymaxrear stopping applies moment to satellite, allows satellite with ω _ymaxcireular frequency carries out constant speed rolling, finally slows down to the maximum torque in satellite time direction, ensure that satellite attitude angle reaches designated value, and attitude angular velocity is 0;

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

t ₁＝t _end-t ₂＝ω _ymax/a _ymax(9)

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

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

t ₂＝θ _m/ω _ymax(10)

Finally, expression formula can be obtained by formula (9) and formula (10)

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

3. a kind of method utilizing satellite pitch axis attitude maneuver to unload 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 accumulated in the process of 45 ° _manu(45 °), satellite is identical by the moment of momentum accumulated in 45 ° of motor-driven processes of 0 ° with satellite by the moment of momentum accumulated in 0 ° of motor-driven process of 45 °, therefore, as motor-driven angle θ _munder the prerequisite of=45 °, the moment of momentum summation accumulated in satellite mobile process is 2h _manu(45 °);

Step 4 two: compare | 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 °) |, then θ _mshould equation be met:

$h_{\mathrm{un}\_y}=2h_{\mathrm{manu}}\left({\mathrm{\&theta;}}_m\right)=\frac{3\mathrm{\&mu;}}{2R^3}(I_z-I_x)\sin 2{\mathrm{\&theta;}}_m{t}_{\mathrm{end}}\left({\mathrm{\&theta;}}_m\right)---\left(12\right)$

In formula, h _manu(θ _m) and t _end(θ _m) represent h _manuwith t _endθ _mfunction, the nonlinear equation solving formula (12) namely can solve required motor-driven angle θ _m, satellite does not keep θ in this case _mprocess, be only fast motor-driven to θ by 0 ° _m, motor-driven to 0 ° more at once, complete unloading.

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

Satellite pitch axis attitude maneuver can be utilized to unload pitch axis moment of momentum, need the inertia of satellite to distribute and satisfy condition:

(1) satellite can provide enough large gravity gradient torque, therefore demand fulfillment condition | I _z-I _x| > > 0;

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

Make a concrete analysis of as follows: if satellite pitch axis actuating unit has moment of momentum at pitch axis and close to saturation value, now need the angular momentum h unloaded _{un_y}<0, now satellite can only provide moment (ensureing that the moment of momentum of mobile process actuating unit does not increase), now satellite can only be motor-driven to θ _m>0, in order to ensure t _hold>0, needs to ensure I according to formula (7) _z<I _x; If in like manner demand fulfillment I can be shifted out equally onto _z<I _x;

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