Method for calculating initial direction of launch of trajectory of carrier rocket by considering trajectory constraint of point under rocket

Abstract

The invention relates to a method for calculating the initial direction of launch of a launch vehicle trajectory by considering the trajectory constraint of a point below a rocket. The method solves the problems of potential safety hazards and disputes caused by the fact that the initial direction of launch of a rocket trajectory is not designed and corrected. 1) coordinate system conversion; 2) calculating the initial direction of launch of the trajectory of the carrier rocket; a launching point of the carrier rocket is known, an area which the rocket lower point track should avoid is determined through map operation, points which the rocket lower point track should experience under the actual condition are determined, and longitude and latitude heights of a target point are obtained through map operation; through coordinate transformation, the coordinate of the connecting line of the target point and the launch point of the carrier rocket in the geocentric fixedly-connected rectangular coordinate system can be obtained; and projecting a connecting line of the target point and the launch point of the carrier rocket to a geographic coordinate system taking the launch point of the carrier rocket as an original point to obtain an azimuth angle of the target point in the geographic coordinate system of the launch point of the carrier rocket. The method is more scientific and accurate than an existing frequently-used experience analogy method.

Description

Technical Field

[0001] This invention relates to a method for calculating the initial trajectory of a launch vehicle considering the trajectory constraints of the launch point, and belongs to the field of launch vehicle trajectory. Background Technology

[0002] In designing a launch vehicle's trajectory, calculating and determining the initial launch direction is a crucial step, as it determines whether the rocket can successfully enter its intended target orbit. Assuming the Earth is a perfect sphere, the following relationship can be obtained using spherical trigonometry formulas. (1) in, For the track inclination angle, This is the launch azimuth angle (the clockwise angle between true north and the launch direction). The latitude of the launch point.

[0003] Once the orbital inclination and launch point latitude are determined, two launch azimuth angles can be calculated using this formula, corresponding to ascending orbit launch (satellite orbit direction is the same as Earth's rotation) and descending orbit launch (satellite orbit direction is opposite to Earth's rotation). Since most of northern China is landmass, the initial launch direction of the launch vehicle is generally chosen to be south; whether it is southeast or southwest depends on the orbital inclination.

[0004] The above scenarios are under ideal conditions, without considering the constraints of the rocket's trajectory. In actual engineering, the rocket's trajectory needs to avoid densely populated areas of the country, the territory and territorial waters (or exclusive economic zones) of other countries, to prevent the rocket from crashing abnormally or causing large-scale casualties or diplomatic disputes due to the fall of first-stage debris.

[0005] If the initial trajectory of the rocket is not designed and corrected, and the theoretical trajectory is used directly, the second stage of the rocket will pass over developed cities, posing a potential safety hazard. Therefore, when designing the trajectory and selecting the trajectory for a launch vehicle, it is necessary to avoid areas with potential hazards. Summary of the Invention

[0006] This invention provides a method for calculating the initial trajectory of a launch vehicle that considers the trajectory constraints of the launch point. This solves the problem that if the initial trajectory of the rocket is not designed and the theoretical trajectory is directly used, the second stage of the rocket will pass over developed cities, posing a potential safety hazard.

[0007] This invention is achieved through the following technical solutions: A method for calculating the initial trajectory of a launch vehicle considering the trajectory constraints of the launch point includes the following steps: 1) Coordinate system transformation 1.1) From the geocentric fixed rectangular coordinate system to the geodetic coordinate system Transformation from geodetic coordinate system to geocentric fixed rectangular coordinate system: (2) Where B is the geodetic latitude, L is the geodetic longitude, and H is the geodetic height. For the Earth's semi-major axis, This is the first eccentricity of the meridian ellipsoid; 1.2) From the geocentric fixed rectangular coordinate system to the geographic coordinate system of the launch site of the carrier rocket The transformation matrix from the North-Eastern geographic coordinate system to the geocentric fixed rectangular coordinate system is: (3) The transformation matrix from the geocentric fixed rectangular coordinate system to the North-Eastern geographic coordinate system is: (4) 2) Calculation of the initial trajectory of the launch vehicle Given the launch site of the launch vehicle, the map operation identifies the area that the rocket's trajectory should avoid, determines the points that the rocket's trajectory will actually pass through, and obtains the latitude, longitude, and altitude of the target point from the map operation. ; The launch site of the carrier rocket has a latitude, longitude, and altitude of [latitude and longitude]. Using formula (2), the coordinates of the target point and the launch point of the carrier rocket in the geocentric fixed rectangular coordinate system are obtained respectively: (5) (6) The coordinates of the line connecting the target point and the launch site of the carrier rocket in the geocentric fixed rectangular coordinate system are: (7) Projecting the line connecting the target point and the launch site onto a geographic coordinate system with the launch site as the origin, we get: (8) The azimuth angle of the target point in the geographic coordinate system of the launch site is: (9) Formula (9) is the initial trajectory of the launch vehicle calculated considering the trajectory constraints of the rocket's ground point, with north-east being positive.

[0008] The beneficial effects of this invention are: 1) Quantitative calculation of the initial trajectory of a rocket considering the trajectory constraints of the launch vehicle's launch point is more scientific and accurate than the empirical analogy method currently used. 2) The calculation method is simple and intuitive, and the physical meaning is obvious. The algorithm is written as a function module. The latitude, longitude and altitude of the launch point of the carrier rocket and the target point of the rocket's trajectory are input. With the powerful matrix operation capability of MATLAB, the calculation can be completed efficiently and quickly. Attached Figure Description

[0009] Figure 1 It is a geodetic coordinate system; Figure 2 It is a geocentric fixed rectangular coordinate system and a launch point geographic coordinate system. Detailed Implementation

[0010] This invention is a method for calculating the initial trajectory of a launch vehicle considering the trajectory constraints of the launch point. Based on the launch position and the trajectory constraints of the launch point, the method determines the initial trajectory of the rocket using the transformation relationship between the geocentric coordinate system and the geographic coordinate system. Specifically, it includes: 1. Coordinate system transformation 1.1 From the geocentric fixed rectangular coordinate system to the geodetic coordinate system Transformation from geodetic coordinate system to geocentric fixed rectangular coordinate system: (2) Where B is the geodetic latitude, L is the geodetic longitude, and H is the geodetic height. The semi-major axis of the Earth can be taken as 6,378,137 m. The first eccentricity of the meridian ellipsoid can be 0.0818191910428.

[0011] 1.2 From the geocentric fixed rectangular coordinate system to the geographic coordinate system of the launch site of the carrier rocket The transformation matrix from the North-Eastern geographic coordinate system to the geocentric fixed rectangular coordinate system is: (3) The transformation matrix from the geocentric fixed rectangular coordinate system to the North-Eastern geographic coordinate system is: (4) 2. Initial trajectory calculation process of launch vehicle Given the launch site of the launch vehicle, map operations identify the area that the rocket's trajectory should avoid, determine the points the rocket's trajectory will actually pass through, and obtain the latitude, longitude, and altitude of the target point from the map operations. .

[0012] The launch site of the carrier rocket has a latitude, longitude, and altitude of [latitude and longitude]. By applying formula (2), the coordinates of the target point and the launch point of the carrier rocket in the geocentric fixed rectangular coordinate system can be obtained respectively. (5) (6) The coordinates of the line connecting the target point and the launch site of the carrier rocket in the geocentric fixed rectangular coordinate system are: (7) Projecting the line connecting the target point and the launch site onto a geographic coordinate system with the launch site as the origin, we can obtain... (8) The azimuth angle of the target point in the geographic coordinate system of the launch site is: (9) Formula (9) is the initial trajectory of the launch vehicle calculated considering the trajectory constraints of the rocket's ground point, with north-east being positive.

[0013] In this invention, the coordinate system is defined as follows: 1. Geodetic Coordinate System like Figure 1 As shown, the geodetic coordinate system The origin is the Earth's center of mass. The axial direction is defined as the point from the origin to the intersection of the Greenwich Meridian and the Earth's equator. The axial direction is defined as the direction from the origin to the Earth's North Pole. An axis is defined as perpendicular to Plane and same axis, The axes form a right-handed coordinate system. The coordinates of any point P in the geodetic coordinate system can be represented as (B, L, H), representing the geodetic latitude, longitude, and geodetic height of point P.

[0014] 2. Geocentric fixed rectangular coordinate system like Figure 2 As shown, the geocentric fixed rectangular coordinate system The coordinate axes completely coincide with the three axes of the geodetic coordinate system. The geodetic coordinate system differs from the geocentric fixed rectangular coordinate system only when representing a single point in space. The coordinates of point P in the geocentric fixed rectangular coordinate system can be expressed as: ,in , , These are OPs (see Figure 1 In a geocentric fixed rectangular coordinate system axis, shaft and Projection value on the axis.

[0015] 3. Geographic coordinate system of launch point Launch point geographic coordinate system origin Defined in the spatial location of the launch site of the carrier rocket. The direction is due north of the launch site of the carrier rocket. The direction it points is the zenith of the location of the launch site of the carrier rocket. The direction is due east of the launch site of the carrier rocket. Figure 2 (Northern Tiandong).

Claims

1. A method for calculating the initial trajectory of a launch vehicle considering the trajectory constraints of the launch point, characterized by: Includes the following steps: 1) Coordinate system transformation 1.1) From the geocentric fixed rectangular coordinate system to the geodetic coordinate system Transformation from geodetic coordinate system to geocentric fixed rectangular coordinate system: Where B is the geodetic latitude, L is the geodetic longitude, H is the geodetic height, a is the Earth's semi-major axis, and e is the first eccentricity of the meridian ellipsoid. 1.2) From the geocentric fixed rectangular coordinate system to the geographic coordinate system of the launch site of the carrier rocket The transformation matrix from the North-Eastern geographic coordinate system to the geocentric fixed rectangular coordinate system is: The transformation matrix from the geocentric fixed rectangular coordinate system to the North-Eastern geographic coordinate system is: 2) Calculation of the initial trajectory of the launch vehicle Given the launch site of the launch vehicle, the map operation identifies the area that the rocket's trajectory should avoid, determines the points that the rocket's trajectory will actually pass through, and obtains the latitude, longitude, and altitude of the target point from the map operation (L). t B t H t ); The launch site of the carrier rocket has a latitude and longitude of (L) m B m H m Using formula (2), the coordinates of the target point and the launch point of the carrier rocket in the geocentric fixed rectangular coordinate system are obtained respectively: x t =(N t +H t )cosB t what is it? t and t =(N t +H t )cosB t sinL t z t =[N t (1-e 2 )+H t ]sinB t (5) The coordinates of the line connecting the target point and the launch site of the carrier rocket in the geocentric fixed rectangular coordinate system are: Projecting the line connecting the target point and the launch site onto a geographic coordinate system with the launch site as the origin, we get: The azimuth angle of the target point in the geographic coordinate system of the launch site is: A0=-atan2(-ΔZ mt_mBTD ,ΔX mt_mBTD ) (9) Formula (9) is the initial trajectory of the launch vehicle calculated considering the trajectory constraints of the rocket's ground point, with north-east being positive.

2. The method for calculating the initial trajectory of a launch vehicle considering the trajectory constraints of the launch point as described in claim 1, characterized in that: In equation (2), a takes the value 6378137m and e takes the value 0.0818191910428.

3. The method for calculating the initial trajectory of a launch vehicle considering the trajectory constraints of the launch point as described in claim 1, characterized in that: The calculation method is written as a function module. The latitude, longitude, and altitude of the launch point and the target point of the rocket's trajectory are input. By utilizing MATLAB's powerful matrix operation capabilities, the calculation can be completed efficiently and quickly.

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