RU2009120762A - METHOD AND DEVICE OF IMITATION OF TRAJECTORIES OF MOVEMENT OF AIR OBJECTS - Google Patents

Abstract

 1. A way to simulate the trajectories of motion of airborne objects by manually entering the initial polar coordinates of the object in the form of bearing П0, range d0, course kob, initial velocity νob and the subsequent automatic formation of the trajectory of motion in the form of a straight line starting from the point (П0; d0) in the direction kob, until the signal arrives at the beginning of the maneuver (turn), synchronous with the introduction of a new course of kob and the speed of the object νob by the time of entering a new course, with imitation of the maneuver (turn) by pairing two straight-line differences directional areas of motion with an arc of a circle whose radius is determined by the rate of change of the course ωk, which is also set at the beginning of the maneuver, characterized in that the simulation of the trajectories of the movement of objects is carried out by manually entering the coordinates of the reference points of the trajectory of movement with an indication of the flight speeds at these points and automatic calculation of equations movement along the three coordinates x (t), y (t), z (t) and speed ϑ (t) immediately after entering the initial data at the operator’s workplace 5 with the subsequent transfer of coefficients these equations into coordinate calculation unit 6, in which, in response to a request for information about the current position of the object, its Cartesian coordinates are calculated by substituting the time parameter t into the equations of motion corresponding to the trajectory section to be overcome at time t, for which the trajectory of the movement of the air object appears to be composed of elementary segments in the form of straight segments, the conjugation of which at an angle between them φ <90 ° is performed with the exception of speed jumps and acceleration by matching sections in the form of

Claims (8)

1. A method of simulating the trajectories of motion of airborne objects by manually entering the initial polar coordinates of the object in the form of bearing П ₀ , range d ₀ , course k _rev , initial velocity ν _rev and subsequent automatic formation of the trajectory of motion in the form of a straight line starting from the point (П ₀ ; d ₀₎ in the direction of k _on, until the receipt of the signal to the beginning of the maneuver (turn), simultaneous with the introduction of a new rate of motion k _on and the speed of the object ν _about the time of entering the new program, with simulated maneuver (turn) by coupling two rectilinear s divergent portions motion arc of a circle whose radius is determined by the speed changing rate ω _k, which is also given at the beginning of the maneuver, characterized in that the simulation trajectories of objects is carried out by manually entering coordinates of control points of the path of movement indicating the flight velocities at these points and automatic of calculating the equations of motion along the three coordinates x (t), y (t), z (t) and speed ϑ (t) immediately after entering the initial data at the workplace of operator 5 with subsequent transfer of the coefficient of these equations to the coordinate calculation unit 6, in which, in response to a request for information about the current position of the object, its Cartesian coordinates are calculated by substituting the time parameter t into the equations of motion corresponding to the trajectory section to be overcome at time t, for which the trajectory of the movement of the air object is represented by elementary segments in the form of straight lines, the conjugation of which at a value of the angle between them φ <90 ° is performed with the exception of speed jumps and acceleration matching sections in the form of an arc of a circle and two segments of cubic parabolas on which the radius of curvature R _k smoothly changes from infinite at the junction points with straight sections to the radius of matching R _c at the junction points with a section in the form of a circular arc or with the exception of the section in the form of a circular arc at of the angle between the coordinated line segments φ≥90 °, calculated in the coordinate calculation unit 6, the Cartesian coordinates of the air object at time t are then converted into polar coordinates in the coordinate transformer 7. 2. The method according to claim 1, characterized in that in the initial section of the transition curve, the conjugation path of line segments is reproduced by a segment of a cubic parabola y = x ³ / 6q with a radius of curvature

providing a smooth (without jumps in speed and acceleration) transition from a straight section at x = 0 and R _k = ∞ to the beginning of the second section with a minimum radius of curvature R _k = R _min . 3. The method according to claim 1, characterized in that when the angle between two straight segments defining the direction of rectilinear movements, φ <90 °, the conjugation path of two straight segments is sequentially divided into three sections: a segment of a cubic parabola, a section of a circular arc with a radius R _min and the third section in the form of a segment of a cubic parabola with a smooth change in the radius of curvature R _k from the value of R _k = R _min to R _k = ∞. 4. The method according to claim 1, characterized in that when the angle between two straight lines defining the direction of rectilinear movements, φ≥90 °, the conjugation path of two straight segments consists of two segments of cubic parabolas with a smooth decrease for the first segment of the radius of curvature R _k from the value of R _k = ∞ to R _c = R _k at the junction and a subsequent increase for the second segment R _k from the value of R _c to R _k = ∞. 5. The method according to claim 1, characterized in that to reproduce the trajectory of movement along an arc of a circle as a function of time t in a rectangular coordinate system, the current values of the coordinates of the object are represented by the parametric equations of the arc of a circle as a function of time. 6. The method according to claim 1, characterized in that when the object moves along a segment of a cubic parabola, the current coordinate values are reproduced as a function of time by replacing the arc of the cubic parabola with an arc of a circle combined with it at three points, with the representation of the values of the x coordinate through a parametric representation of the coordinate x (t) of the circle and the expression of the values of the coordinate y (t) in terms of the coordinate x (t) in accordance with the equation of the cubic parabola. 7. A device for simulating the trajectories of motion of air objects, containing the teacher’s console 1, the first output of which is connected to the first input of the coordinate transformer 2, and the second output is connected to the first input of the smoothing block 3, the second input of which is connected to the first output of the coordinate transformer 2, the output of the smoothing unit 3 is connected to the second input of the coordinate converter 2, the second output of the coordinate converter 2 is connected to the input of the operator panel 4 with a built-in remote panoramic indicator for tracking and calculating the ordinate of the object, characterized in that the teacher’s console is designed as an operator’s workstation 5 based on a PC-like computer, the output of which is connected to the input of the coordinate calculation unit 6, the output of the coordinate calculation unit 6 is connected to the input of the coordinate converter 7. 8. The device according to claim 7, characterized in that the coordinate calculation unit 6 comprises an input interface for external requests.