CN114485265A - Method for designing bending section trajectory of electromagnetic launch rocket - Google Patents

Method for designing bending section trajectory of electromagnetic launch rocket Download PDF

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CN114485265A
CN114485265A CN202111491238.5A CN202111491238A CN114485265A CN 114485265 A CN114485265 A CN 114485265A CN 202111491238 A CN202111491238 A CN 202111491238A CN 114485265 A CN114485265 A CN 114485265A
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angle
axis
coordinate system
rocket
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CN114485265B (en
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李晓苏
汪潋
黎桪
邹延兵
左湛
周鑫
黄晓平
唐梦莹
刘李雷
杨凯铜
王志军
岳小飞
刘克龙
段淑婧
彭彦召
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CASIC Rocket Technology Co
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41—WEAPONS
    • F41F—APPARATUS FOR LAUNCHING PROJECTILES OR MISSILES FROM BARRELS, e.g. CANNONS; LAUNCHERS FOR ROCKETS OR TORPEDOES; HARPOON GUNS
    • F41F3/00—Rocket or torpedo launchers
    • F41F3/04—Rocket or torpedo launchers for rockets
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41—WEAPONS
    • F41F—APPARATUS FOR LAUNCHING PROJECTILES OR MISSILES FROM BARRELS, e.g. CANNONS; LAUNCHERS FOR ROCKETS OR TORPEDOES; HARPOON GUNS
    • F41F3/00—Rocket or torpedo launchers
    • F41F3/04—Rocket or torpedo launchers for rockets
    • F41F3/0406—Rail launchers
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention relates to a method for designing a trajectory of a turning section of an electromagnetic launch rocket, which comprises the following steps: defining a launch system, defining an arrow system, establishing a new coordinate system with respect to the launch system, establishing a new coordinate system in the new coordinate system OX2Y2Z2Designing a new attack angle and a new sideslip angle, and calculating a new attitude angle under a new coordinate system; and converting the new attitude angle under the new coordinate system into the attitude angle of the launching system. When the target orbit inclination angle is greatly different from the rocket launching, the method of the invention can smoothly realize large-amplitude lateral turning so as to meet the requirements of various orbit inclination angles under the condition of fixed launching.

Description

Method for designing trajectory of turning section of electromagnetic launch rocket
Technical Field
The invention belongs to the technical field of rocket trajectory design, and particularly relates to a method for designing a trajectory of a turning section of an electromagnetic launch rocket.
Background
Compared with the traditional rocket launching mode, the electromagnetic launching technology has the biggest difference that once the electromagnetic launching guide rail is built, the instantaneous azimuth angle of the rocket separated from the guide rail cannot be changed, namely the rocket launching is a fixed value, the traditional launching mode can match the target orbit inclination angle due to the launching, gravity turning can be realized only by designing the attack angle in the turning section trajectory design, and for the electromagnetic launching mode with fixed launching direction, if lateral maneuvering is not carried out, the satellite is only sent into the non-specified inclination angle orbit, then a large amount of fuel is consumed by changing the inclination angle depending on the satellite, so that the rocket is required to turn by means of the thrust of an engine and aerodynamic force when the speed is not high after the rocket is derailed. When the target orbit inclination angle is greatly different from the rocket launching angle, the traditional mode of adding the sideslip angle cannot realize large-amplitude side turning.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a novel turning section trajectory design method, so that the turning section trajectory design method can meet various track inclination angle requirements under the fixed direction condition.
In order to achieve the purpose, the invention provides a method for designing a trajectory of a turning section of an electromagnetic launch rocket, which is characterized in that the method for designing the trajectory of the turning section of the rocket after the rocket enters the turning section comprises the following steps
Defining a transmitting system, wherein the origin of coordinates of an transmitting coordinate system OXYZ is positioned at the transmitting origin, an OY axis is a plumb line passing through a transmitting point, the plumb line is positive, an OX axis is vertical to the OY axis and points to the theoretical direction, and a right-hand rectangular coordinate system is formed by the OZ axis, the OX axis and the OY axis;
defining an arrow system, wherein the origin of coordinates of the arrow system OX1YZ1 is located at the center of mass of the rocket, the axis OX1 is consistent with the longitudinal symmetry axis of the arrow body and points to the head direction, the axis OY1 is perpendicular to the axis OX1 and is located in the longitudinal symmetry plane of the rocket and points upwards, and the axis OZ1, the axis OX1 and the axis OY1 form a right-hand rectangular coordinate system;
establishing a new coordinate system relative to the emission system, the origin of the new coordinate system coinciding with the origin of the emission system, Y of the new coordinate system2The axis coincides with the Y-axis of the emitter system, X2The axis being around Y2The axis rotating with the horizontal velocity component of the arrow body, X2The axis pointing forward in the direction of the horizontal component of rocket velocity, Z2The axis is determined by the right hand rule;
in a new coordinate system OX2Y2Z2Designing a new attack angle and a new sideslip angle, wherein the new attack angle refers to an arrow body longitudinal axis OX1Axis in new coordinate system X2OY2Projection of plane and OX2The new sideslip angle refers to the rocket longitudinal axis OX1Axes and new coordinate system X2OY2The included angle of the plane;
calculating a new attitude angle under a new coordinate system;
and converting the new attitude angle under the new coordinate system into the attitude angle of the launching system.
Further, the new angle of attack α 1(t) is calculated as follows:
Figure BDA0003399441310000021
when ballistic design is calculated, a new attack angle is added in a [ t1, t2] interval, the new attack angle is in a parabolic form, and the new attack angle returns to zero when the new attack angle is larger than t 2;
novel sideslip angle beta1(t) the calculation formula is as follows:
Figure BDA0003399441310000022
when ballistic design is calculated, adding a new sideslip angle in a [ t3, t4] interval, wherein the new sideslip angle is a constant value, and the new sideslip angle returns to zero after the new sideslip angle is larger than t 4;
wherein alpha isk、βkThe two design values respectively present monotone increasing and monotone decreasing relations with the orbit semimajor axis and the orbit inclination angle as design values, the requirements of the orbit semimajor axis and the orbit inclination angle are met by adjusting the two values, and the iterative formula is as follows:
Figure BDA0003399441310000031
wherein:
i- -Current track Tilt;
a-current orbit semi-major axis;
IMB-a target orbit inclination;
aMB-target track semi-major axis.
Further, said α isk、βkThe initial value of (A) is generally in the range of [ -20 DEG, 20 DEG ]]、 [-30°、30°]。
Further, the method for calculating the attitude angle in the newly defined coordinate system comprises the following steps:
and transferring the transmitting system speed calculated in the integration process to a newly defined coordinate system in the following calculation mode:
the angle through which the newly defined coordinate system rotates with respect to the transmission system, i.e. the angle to which the current velocity component is directed, is calculated as follows:
Figure BDA0003399441310000032
the transmit system velocity [ Vfx, Vfy, Vfz ] is transferred to the new coordinate system [ Vx, Vy, Vz ], calculated as follows:
Figure BDA0003399441310000033
and calculating a new trajectory inclination angle theta and a new trajectory deflection angle sigma under a new coordinate system, wherein the new trajectory deflection angle sigma is zero because the new coordinate is always in the incidence plane, and the new trajectory inclination angle is calculated as follows:
Figure BDA0003399441310000034
calculating a new pitch angle in a new coordinate system
Figure BDA0003399441310000041
And a new yaw angle ψ, calculated as follows:
Figure BDA0003399441310000042
ψ＝β1(t)
and (5) setting the new roll angle lambda as 0 in the new coordinate system.
Further, the specific conversion method for converting the new attitude angle in the new coordinate system into the attitude angle in the original defined coordinate system (emission system) is as follows:
new pitch angle from new coordinate system
Figure BDA0003399441310000043
Calculating the pitch angle under the transmitting system according to the new yaw angle psi
Figure BDA0003399441310000044
And yaw angle psifThe calculation method is as follows,
and calculating a coordinate transformation matrix from an arrow system to a newly defined coordinate system, wherein the calculation is as follows:
Figure BDA0003399441310000045
MDT2FS1＝MFS12DT -1
and calculating a coordinate transformation matrix from the new coordinate system to the emission system, wherein the calculation is as follows:
Figure BDA0003399441310000046
calculating the pitch angle of the transmitting system
Figure BDA0003399441310000047
With yaw angle psifThe calculation method is as follows: arrow system X1Axial unit vector [1,0]The light beam is projected to the emission system,
Figure BDA0003399441310000048
Figure BDA0003399441310000051
ψf＝-arcsin(rz)。
the attitude angle, namely the pitch angle, of the transmitting system obtained by calculation
Figure BDA0003399441310000052
With yaw angle psifThe method is used for calculating the trajectory of the turning section when the rocket is separated from the guide rail or separated from the electromagnetic launching guide rail and the speed is not high, and meets the design requirement.
In the traditional method, the turning design is carried out by adding the attack angle and the sideslip angle, and the attitude angle of the rocket is obtained by adding the attack angle and the sideslip angle on the basis of the trajectory inclination angle and the trajectory deflection angle (calculated under a launching system), wherein the trajectory inclination angle describes the included angle between the velocity vector of the rocket and the horizontal plane, and the trajectory deflection angle describes the included angle between the velocity vector and the shooting plane. However, when the lateral turning angle is large, the x-axis component of the launching system of the rocket horizontal velocity is smaller and smaller along with the lateral turning of the rocket, and the ballistic inclination angle is the arc tangent of the Y-direction velocity of the launching system divided by the x-direction velocity
Figure BDA0003399441310000053
Then the trajectory inclination angle calculated in the turning section may increase (actually the trajectory inclination angle in the turning section should be smaller and smaller in the turning process), assuming that in the limit state, the speed rotates laterally by 90 °, at this time, the component of the horizontal speed on the x-axis of the launching system is 0, the calculated trajectory inclination angle is 90 °, and the rocket from the ignition to the end of the turning section generally only may have the speed inclination angle of 90 ° at the moment of ignition, and may not return to 90 ° at other times. The above problem arises from the natural drawback of the rotation of the coordinate system 3-2-1 (first the z axis, then the Y axis and finally the X axis) in the case of excessive lateral manoeuvres.
The method of the invention carries out ballistic trajectory design in the turning stage depending on the thrust and aerodynamic force of the engine when the rocket is not at a high speed after derailing, and establishes a new coordinate system, wherein X of the new coordinate system2The axis being around Y2The axis rotates along with the direction of the horizontal velocity component of the rocket body, namely, the axis continuously changes in the flying process of the rocket, a new attack angle and a new sideslip angle are designed in a new coordinate system, a new attitude angle under the newly defined coordinate system is calculated, and finally the new attitude angle under the newly defined coordinate system is converted into a launching system attitude angle for ballistic design calculation.
Drawings
FIG. 1 is a schematic view of arrow system coordinates;
fig. 2 is a diagram of a newly defined coordinate system.
In the figure, α and β respectively refer to an attack angle and a sideslip angle designed in a launching system, α 1 and β 1 respectively refer to a "new attack angle α 1 (t)" and a "new sideslip angle β 1 (t)" designed in a new coordinate system, and a triangle is a rocket body structure schematic diagram.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a method for designing a trajectory of a turning section of an electromagnetic launch rocket, wherein the method comprises the following steps of designing the trajectory of the turning section after the rocket enters the turning section
Firstly, defining a transmitting system, wherein the origin of coordinates of an transmitting coordinate system OXYZ is positioned at the transmitting origin, an OY axis is a plumb line passing through a transmitting point, the plumb line is positive upwards, an OX axis is vertical to the OY axis and points to the theoretical direction, and a right-hand rectangular coordinate system is formed by the OZ axis, the OX axis and the OY axis;
as shown in fig. 1, an arrow system is defined, an origin of coordinates of an arrow system OX1YZ1 is located at a rocket center of mass, an axis OX1 is consistent with a longitudinal symmetry axis of an arrow body and points to a head direction, an axis OY1 is perpendicular to an axis OX1 and is located in the longitudinal symmetry plane of the rocket and points upwards, and an axis OZ1, an axis OX1 and an axis OY1 form a right-hand rectangular coordinate system;
in general, the angle of attack α is defined as the projection of the velocity vector V onto the main plane of symmetry of the rocket and the longitudinal axis of the rocket body (OX)1Axis) and sideslip angle beta refers to the velocity vector V and the rocket primary symmetry plane (X)1OY1) As shown in fig. 1;
FIG. 2 shows that a new coordinate system is established with respect to the transmit system, the origin of the new coordinate system coinciding with the origin of the transmit system, Y of the new coordinate system2The axis coincides with the Y-axis of the emitter system, X2Axis of rotation about Y2The axis rotating with the horizontal velocity component of the arrow body, X2The axis pointing forward in the direction of the horizontal component of rocket velocity, Z2The axis is determined by the right hand rule;
designing a new attack angle and a new sideslip angle in a new coordinate system;
the new angle of attack alpha1Refers to the longitudinal axis (OX) of the arrow body1Axis) in a newly defined coordinate system X2OY2Projection of plane and OX2The included angle of (A);
the new sideslip angle beta1Refers to the rocket longitudinal axis (OX)1Axis) and the newly defined coordinate system X2OY2The included angle of the plane;
the new angle of attack α 1(t) is calculated as follows:
Figure BDA0003399441310000071
when ballistic design is calculated, the new attack angle is added in the interval of [ t1, t2], the attack angle is in a parabolic form, and the new attack angle returns to zero after the attack angle is larger than t 2; the time interval of [ t1, t2] is generally in the time period of not high speed after the rocket derails;
novel sideslip angle beta1(t) the calculation formula is as follows:
Figure BDA0003399441310000072
when ballistic design is calculated, adding the new sideslip angle in the interval [ t3, t4], wherein the new sideslip angle is a constant value, and the new sideslip angle returns to zero after the new sideslip angle is larger than t 4; the time interval of [ t3, t4] is generally in the time period of not high speed after the rocket derails;
wherein alpha isk、βkThe two design values respectively show monotone increasing and monotone decreasing relations with the semi-major axis of the track and the track inclination angle, the requirements of the semi-major axis of the track and the track inclination angle are met by adjusting the two values, alphak、βkThe iterative formula is as follows:
Figure BDA0003399441310000081
wherein:
i- -Current track Tilt;
a-current orbit semi-major axis;
IMB-a target orbit inclination;
aMB-a target track semi-major axis;
αk、βkthe initial value of (A) is generally in the range of [ -20 DEG, 20 DEG ]]、[-30°、30°]。
Calculating an attitude angle under the newly defined coordinate system;
the calculation method of the new attitude angle under the newly defined coordinate system comprises the following steps:
and transferring the transmitting system speed calculated in the integration process to a newly defined coordinate system, wherein the calculation mode is as follows:
the angle through which the newly defined coordinate system rotates with respect to the transmission system, i.e. the angle to which the current velocity component is directed, is calculated as follows:
Figure BDA0003399441310000082
the transmit system velocity [ Vfx, Vfy, Vfz ] is transferred to the newly defined coordinate system [ Vx, Vy, Vz ], calculated as follows:
Figure BDA0003399441310000083
and calculating a new trajectory inclination angle theta and a new trajectory deflection angle sigma under a new coordinate system, wherein the new trajectory deflection angle sigma is zero because the new coordinate is always in the incidence plane, and the new trajectory inclination angle is calculated as follows:
Figure BDA0003399441310000084
calculating a new pitch angle in a new coordinate system
Figure BDA0003399441310000085
And a new yaw angle ψ, calculated as follows:
Figure BDA0003399441310000091
ψ＝β1(t)
let the new roll angle λ be 0 in the new coordinate system.
And converting the attitude angle under the newly defined coordinate system into the attitude angle of the original defined coordinate system.
The specific conversion method for converting the new attitude angle under the new coordinate system into the attitude angle of the launching system is as follows:
new pitch angle from new coordinate system
Figure BDA0003399441310000092
Calculating the pitch angle under the transmitting system according to the new yaw angle psi
Figure BDA0003399441310000093
And yaw angle psifThe calculation method is as follows,
and calculating a coordinate transformation matrix from an arrow system to a new coordinate system, wherein the calculation is as follows:
Figure BDA0003399441310000094
MDT2FS1＝MFS12DT -1
and calculating a coordinate transformation matrix from the new coordinate system to the emission system, wherein the calculation is as follows:
Figure BDA0003399441310000095
calculating the pitch angle of the transmitting system
Figure BDA0003399441310000096
With yaw angle psifThe calculation method is as follows: arrow system X1Axial unit vector [1,0]The light beam is projected to the emission system,
Figure BDA0003399441310000097
Figure BDA0003399441310000101
ψf＝-arcsin(rz)。
calculating the attitude angle, namely the pitch angle of the transmitting system
Figure BDA0003399441310000102
With yaw angle psifThe method is used for calculating the trajectory of the turning section when the initial speed of the rocket is not large after derailing, and meets the design requirements.

Claims (5)

1. A method for designing a turning section trajectory of an electromagnetic launch rocket is characterized in that the turning section trajectory design is carried out after the rocket enters a turning section, and the method comprises the following steps
Defining a transmitting system, wherein the origin of coordinates of an transmitting coordinate system OXYZ is positioned at the transmitting origin, an OY axis is a plumb line passing through a transmitting point, the plumb line is positive, an OX axis is vertical to the OY axis and points to the theoretical direction, and a right-hand rectangular coordinate system is formed by the OZ axis, the OX axis and the OY axis;
defining an arrow system, wherein the origin of coordinates of the arrow system OX1YZ1 is located at the center of mass of the rocket, the axis OX1 is consistent with the longitudinal symmetry axis of the arrow body and points to the head direction, the axis OY1 is perpendicular to the axis OX1 and is located in the longitudinal symmetry plane of the rocket and points upwards, and the axis OZ1, the axis OX1 and the axis OY1 form a right-hand rectangular coordinate system;
establishing a new coordinate system relative to the emission system, the origin of the new coordinate system coinciding with the origin of the emission system, Y of the new coordinate system2The axis coincides with the Y-axis of the emitter system, X2The axis being around Y2The axis rotating with the horizontal velocity component of the arrow body, X2The axis points forward to the rocket velocity horizontal component direction, Z2The axis is determined by the right hand rule;
in a new coordinate system OX2Y2Z2Designing a new attack angle and a new sideslip angle, wherein the new attack angle refers to an arrow body longitudinal axis OX1Axis in new coordinate system X2OY2Projection of plane and OX2The new sideslip angle refers to the rocket longitudinal axis OX1Axis and new coordinate system X2OY2The included angle of the plane;
calculating a new attitude angle under a new coordinate system;
and converting the new attitude angle under the new coordinate system into the attitude angle of the launching system.
2. A rocket turning section ballistic design method according to claim 1, characterized in that said new angle of attack α1(t) the calculation formula is as follows:
Figure FDA0003399441300000011
when ballistic design is calculated, a new attack angle is added in a [ t1, t2] interval, the attack angle is in a parabolic form, and the new attack angle returns to zero when the attack angle is larger than t 2;
novel sideslip angle beta1(t) the calculation formula is as follows:
Figure FDA0003399441300000012
when ballistic design is calculated, adding a new sideslip angle in a [ t3, t4] interval, wherein the new sideslip angle is a constant value, and the new sideslip angle returns to zero after the new sideslip angle is larger than t 4;
wherein alpha isk、βkThe two design values respectively present monotonously increasing and monotonously decreasing relations with the track semimajor axis and the track inclination angle as design values, the requirements of the track semimajor axis and the track inclination angle are met by adjusting the two values, and the iterative formula is as follows:
Figure FDA0003399441300000021
wherein:
i- -Current track Tilt;
a- -current track semi-major axis;
IMB-a target orbit inclination;
aMB-target track semi-major axis.
3. A rocket turning segment ballistic design method according to claim 2, wherein said α isk、βkThe initial value of (A) is generally in the range of [ -20 DEG, 20 DEG ]]、[-30°、30°]。
4. A rocket turning segment ballistic design method according to claim 1, wherein the new attitude angle under the newly defined coordinate system is calculated by:
and transferring the transmitting system speed calculated in the integration process to a new coordinate system, wherein the calculation mode is as follows:
the angle through which the new coordinate system rotates relative to the transmitting system, i.e. the angle to which the current velocity component is directed, is calculated as follows:
Figure FDA0003399441300000022
the transmit system velocity [ Vfx, Vfy, Vfz ] is transferred to the new coordinate system [ Vx, Vy, Vz ], calculated as follows:
Figure FDA0003399441300000031
and calculating a new trajectory inclination angle theta and a new trajectory deflection angle sigma under a new coordinate system, wherein the new trajectory deflection angle sigma is zero because the new coordinate is always in the incidence plane, and the new trajectory inclination angle is calculated as follows:
Figure FDA0003399441300000032
calculating a new pitch angle in a new coordinate system
Figure FDA0003399441300000033
And a new yaw angle ψ, calculated as follows:
Figure FDA0003399441300000034
ψ＝β1(t)
and (5) setting the new roll angle lambda as 0 in the new coordinate system.
5. The rocket turning segment ballistic design method according to claim 4, characterized in that the specific transformation method for transforming the new attitude angle under the new coordinate system into the launch system attitude angle is as follows:
new pitch angle from new coordinate system
Figure FDA0003399441300000035
Calculating the pitch angle under the transmitting system according to the new yaw angle psi
Figure FDA0003399441300000036
And yaw angle psifThe calculation method is as follows,
and calculating a coordinate transformation matrix from an arrow system to a new coordinate system, wherein the calculation is as follows:
Figure FDA0003399441300000037
MDT2FS1＝MFS12DT -1
and calculating a coordinate transformation matrix from the new coordinate system to the emission system, wherein the calculation is as follows:
Figure FDA0003399441300000038
calculating the pitch angle of the transmitting system
Figure FDA0003399441300000041
With yaw angle psifThe calculation method is as follows: arrow system X1Axial unit vector [1,0]The light beam is projected to the emission system,
Figure FDA0003399441300000042
Figure FDA0003399441300000043
ψf＝-arcsin(rz)。
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王传魁;周文勇;陈益;张利宾;解永锋;: "基于转动矩阵法的火箭上面级机动程序角设计" *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116719333A (en) * 2023-05-25 2023-09-08 西安现代控制技术研究所 Design method for vertical-launching missile speed vector control turning instruction

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