CN114485265B - Method for designing bending section trajectory of electromagnetic launch rocket - Google Patents
Method for designing bending section trajectory of electromagnetic launch rocket Download PDFInfo
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- CN114485265B CN114485265B CN202111491238.5A CN202111491238A CN114485265B CN 114485265 B CN114485265 B CN 114485265B CN 202111491238 A CN202111491238 A CN 202111491238A CN 114485265 B CN114485265 B CN 114485265B
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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
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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
- F41F3/0406—Rail launchers
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- 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
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Abstract
The invention relates to a method for designing a bending section trajectory 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 OX 2 Y 2 Z 2 Designing 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 an emission system attitude angle. When the target orbit inclination angle is greatly different from the rocket shooting angle, 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 fixed shooting condition.
Description
Technical Field
The invention belongs to the technical field of rocket trajectory design, and particularly relates to a trajectory design method for a turning section of an electromagnetic launch rocket.
Background
Compared with the traditional rocket launching mode, the electromagnetic launching technology has the greatest 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, in the traditional launching mode, the launching can be matched with the target orbit inclination angle, the gravity turning is realized only by designing an attack angle in the turning section trajectory design, and in the electromagnetic launching mode with fixed launching direction, if no lateral maneuver is performed, the satellite is only sent into an unspecified inclination angle orbit, then the satellite is used for changing the inclination angle, a large amount of fuel is consumed, and the rocket needs to turn by the thrust of an engine and the aerodynamic force when the speed is not high after the rocket is separated from the orbit. 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 turning section trajectory of an electromagnetic launch rocket, which is characterized in that the turning section trajectory design is carried out after the rocket enters the 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 an OX1YZ1 of the arrow system is positioned in the center of mass of the rocket, the axis of OX1 is consistent with the longitudinal symmetry axis of the rocket body and points to the head direction, the axis of OY1 is vertical to the axis of OX1 and positioned in the longitudinal symmetry plane of the rocket and points to the upper direction, and the axis of OZ1, the axis of OX1 and the axis of 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 system 2 The axis coincides with the Y-axis of the emitter system, X 2 Axis of rotation about Y 2 The axis rotating with the horizontal velocity component of the arrow body, X 2 The axis points forward to the rocket velocity horizontal component direction, Z 2 The axis is determined by the right hand rule;
in a new coordinate system OX 2 Y 2 Z 2 Designing a new attack angle and a new sideslip angle, wherein the new attack angle refers to an arrow body longitudinal axis OX 1 Axis in new coordinate system X 2 OY 2 Projection of plane and OX 2 The new sideslip angle is the rocket longitudinal axis OX 1 Axes and new coordinate system X 2 OY 2 The 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:
when trajectory design calculation is carried out, a new attack angle is added in a [ t1, t2] interval, the new attack angle is in a parabola form, and the new attack angle returns to zero when the new attack angle is larger than t 2;
novel sideslip angle beta 1 (t) the calculation formula is as follows:
when trajectory design calculation is carried out, adding a new sideslip angle in a [ t3, t4] interval, wherein the new sideslip angle is a constant value, and enabling the new sideslip angle to return to zero after the new sideslip angle is larger than t 4;
wherein alpha is k 、β k To design valueThe two design values respectively present monotone increasing and monotone decreasing relations with the track semimajor axis and the track inclination angle, 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:
wherein:
i- -Current track Tilt;
a- -current track semi-major axis;
I MB -a target orbit inclination;
a MB -target track semi-major axis.
Further, the alpha is k 、β k The initial value of (A) is generally in the range of [ -20 DEG, 20 DEG ]]、 [-30°、30°]。
Further, the calculation method of the attitude angle in the newly defined coordinate system includes:
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:
the transmit system velocity [ Vfx, vfy, vfz ] is transferred to the new coordinate system [ Vx, vy, vz ] by the following calculation:
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:
calculating a new pitch angle in a new coordinate system
And a new yaw angle ψ, calculated as follows:
ψ＝β 1 (t)
let the new roll angle λ =0 in the new coordinate system.
Further, the specific method for converting the new attitude angle in the new coordinate system into the attitude angle in the originally defined coordinate system (emission system) is as follows:
new pitch angle from new coordinate system
And a new yaw angle psi, calculating a pitch angle in the launch system>
And yaw angle psi f The 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:
M DT2FS1 ＝M FS12DT -1
and calculating a coordinate conversion matrix from the new coordinate system to the transmitting system, wherein the calculation is as follows:
calculating the pitch angle of the transmitting system
With yaw angle psi f The calculation method is as follows: arrow system X 1 Axial unit vector [1,0]The light is projected onto the light-emitting system,
ψ f ＝-arcsin(r z )。
calculating the attitude angle, namely the pitch angle of the transmitting system
With yaw angle psi f The method is used for calculating the trajectory of a 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
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 trajectory design in the turning stage depending on the thrust and the aerodynamic force of the engine when the rocket is not at a high speed after derailment, establishes a new coordinate system and the X of the new coordinate system 2 Axis of rotation about Y 2 The 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 do not limit the invention. In addition, the technical features involved in the respective 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 turning section trajectory of an electromagnetic launch rocket, wherein the turning section trajectory design is carried out after the rocket enters a turning section, and the method comprises the following steps
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 of OX1 is consistent with a longitudinal symmetry axis of an arrow body and points to a head direction, an axis of OY1 is perpendicular to the axis of OX1 and located in the longitudinal symmetry plane of the rocket and points to the upper direction, and an axis of OZ1, the axis of OX1 and the axis of 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) 1 Axis) and sideslip angle beta refers to the velocity vector V and the rocket primary symmetry plane (X) 1 OY 1 ) 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 system 2 The axis coincides with the Y-axis of the emitting system, X 2 The axis being around Y 2 The axis rotating with the horizontal velocity component of the arrow body, X 2 The axis pointing forward in the direction of the horizontal component of rocket velocity, Z 2 The 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 alpha 1 Refers to the longitudinal axis (OX) of the arrow body 1 Axis) in a newly defined coordinate system X 2 OY 2 Projection of plane and OX 2 The included angle of (c);
the new sideslip angle beta 1 Refers to the rocket longitudinal axis (OX) 1 Axis) and the newly defined coordinate system X 2 OY 2 The included angle of the plane;
the new angle of attack α 1 (t) is calculated as follows:
when trajectory design calculation is carried out, the new attack angle is added in a [ t1, t2] interval, the attack angle is in a parabola form, and the new attack angle returns to zero when the attack angle is larger than t 2; the [ t1, t2] time interval is generally in the time period of low speed after the rocket derails;
novel sideslip angle beta 1 (t) the calculation formula is as follows:
when trajectory design calculation is carried out, adding the new sideslip angle in a [ t3, t4] interval, wherein the new sideslip angle is a constant value, and enabling the new sideslip angle to return to zero after the new sideslip angle is larger than t 4; the [ t3, t4] time interval is generally in the time period of low speed after the rocket derails;
wherein alpha is k 、β k The 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, alpha k 、β k The iterative formula is as follows:
wherein:
i- -Current track Tilt;
a-current orbit semi-major axis;
I MB -a target orbital inclination;
a MB -a target track semi-major axis;
α k 、β k the 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:
the transmit system velocity [ Vfx, vfy, vfz ] is transferred to the newly defined coordinate system [ Vx, vy, vz ] by the following calculation:
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:
calculating a new pitch angle in a new coordinate system
And a new yaw angle ψ, calculated as follows:
ψ＝β 1 (t)
let the new roll angle λ =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
And the new yaw angle psi, calculating the pitch angle in the launch train>
And yaw angle psi f The 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:
M DT2FS1 ＝M FS12DT -1
and calculating a coordinate transformation matrix from the new coordinate system to the emission system, wherein the calculation is as follows:
calculating the pitch angle of the transmitting system
With yaw angle psi f The calculation method is as follows: arrow system X 1 Axial unit vector [1,0]The light beam is projected to the emission system,
ψ f ＝-arcsin(r z )。
the attitude angle, namely the pitch angle, of the transmitting system obtained by calculation
With yaw angle psi f The 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 (1)
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;
definition of arrow System, arrow System OX 1 Y 1 Z 1 Its origin of coordinates is located at rocket centroid, OX 1 The axis and the longitudinal direction of the arrowThe axes of symmetry being coincident and pointing in the direction of the head, OY 1 Axis perpendicular to OX 1 Axis, located in the longitudinal symmetry plane of the rocket, pointing upwards, OZ 1 Shaft and OX 1 Shaft, OY 1 The axes 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 system 2 The axis coincides with the Y-axis of the emitter system, X 2 The axis being around Y 2 The axis rotating with the horizontal velocity component of the arrow body, X 2 The axis pointing forward in the direction of the horizontal component of rocket velocity, Z 2 The axis is determined by the right hand rule;
in a new coordinate system OX 2 Y 2 Z 2 Designing a new attack angle and a new sideslip angle, wherein the new attack angle refers to a longitudinal axis OX of the rocket body 1 Axis in a new coordinate system X 2 OY 2 Projection of plane and OX 2 The new sideslip angle refers to the rocket longitudinal axis OX 1 Axes and new coordinate system X 2 OY 2 The included angle of the plane;
calculating a new attitude angle under a new coordinate system;
converting the new attitude angle under the new coordinate system into an emission system attitude angle;
the new angle of attack alpha 1 (t) the calculation formula is as follows:
in ballistic design calculation, at [ t ] 1 ,t 2 ]A new attack angle is added in the interval, the attack angle is in a parabolic form and is larger than t 2 Then, the new attack angle returns to zero;
new sideslip angle beta 1 (t) calculated as follows:
in ballistic design calculation, at [ t ] 3 ,t 4 ]Adding a new sideslip angle into the interval, wherein the new sideslip angle is a constant value,greater than t 4 Then, the new sideslip angle returns to zero;
wherein alpha is k 、β k The 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:
wherein:
i- -Current track Tilt;
a- -current track semi-major axis;
I MB -a target orbital inclination;
a MB -a target track semi-major axis;
a is said k 、β k The initial value of (A) is generally in the range of [ -20 DEG, 20 DEG ]]、[-30°、30°]；
The method for calculating the new attitude angle in the new coordinate system comprises the following steps:
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 with respect to the transmission system, i.e. the angle to which the current velocity component is directed, is calculated as follows:
transferring the transmitting system speed [ Vfx, vfy, vfz ] to a new coordinate system [ Vx, vy, vz ] by the following calculation mode:
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 incident plane, and the new trajectory inclination angle is calculated as follows:
calculating a new pitch angle in a new coordinate system
And a new yaw angle ψ, calculated as follows:
ψ＝β 1 (t)
enabling a new roll angle lambda =0 in a new coordinate system;
the specific conversion method for converting the new attitude angle in the new coordinate system into the attitude angle of the launching system is as follows:
new pitch angle from new coordinate system
And the new yaw angle psi, calculating the pitch angle in the launch train>
And yaw angle psi f The calculation method is as follows,
and calculating a coordinate conversion matrix from an arrow system to a new coordinate system, wherein the calculation is as follows:
M DT2FS1 ＝M FS12DT -1
and calculating a coordinate transformation matrix from the new coordinate system to the emission system, wherein the calculation is as follows:
calculating the pitch angle of the transmitting system
With yaw angle psi f The calculation method is as follows: arrow system X 1 Axial unit vector [1,0]Projected to the emitting system, and then>
ψ f ＝-arcsin(r z )。
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