Nutation is an astronomical term.When the gyro rotatesangular velocityIf it is not large enough, it will not only rotate andPrecessionExternalAxis of symmetryIt will also swing up and down in the vertical plane, called nutation.
Nutation values can generally be divided into parallel and perpendicularEclipticThe two components of the ecliptic are calledNutation of yellow meridianThe component of the vertical ecliptic is called oblique nutation.
precession of the equinoxesAnd nutationTrue celestial poleAround the yellow polecelestial sphereDraw a wavy curve on it.In addition, the coupling motion of nutation and precession is the main factor that affects the stability of the conical motion of rockets.
The elliptical trajectory generated by the instantaneous north celestial pole rotating around the instantaneous horizontal north celestial pole.Astronomically, the celestial pole is relative toYellow poleExcept those with long periodsprecession of the equinoxesIn addition to changes, there are many small changes with short periods.The reason for this change is that the position of the earth relative to the moon and the sun has periodic changes, and the gravitational action it receives from the latter two also has the same periodic changes, so thatearth rotationIn addition to the long-term slow movement (precession), the spatial direction of the axis is also superimposed with small amplitude vibration of various periods, which is called nutation.
Nutation values can generally be divided into parallel and perpendicularEclipticThe two components of the ecliptic are calledNutation of yellow meridianThe component of the vertical ecliptic is called oblique nutation.becausecelestial sphereThe coordinate system is based on the equator and the equinox, which also means that the earth's equator is projected outward to the big circle on the celestial sphere, and the intersection of a line on the circle is calledVernal equinoxIs the starting position of right ascension measurement, and this point will be dividedprecession of the equinoxesAnd nutation, so theoretically the values of precession and nutation also need to depend on the date referenced by the coordinate system.In simpler terms, it is necessary to calculate theVisual position, nutation (andprecession of the equinoxes）The value of is a very important item.
NutationVernal equinoxOn the ecliptic andYellow declination angleFor their respective average positions, periodic oscillations occur, with amplitudes of 17 ''2 and 9''2, respectively.Therefore, the coordinates of celestial bodies, such as right ascension and declination, change.
Impact on missile body
Bullet bodySpinning is conducive to eliminating thrust eccentricity, enhancing flight stability of the missile body, and improving shooting accuracy, but it will also bring other problems that non spin missiles do not have, such as additional Magnus effect, serious coupling between channels caused by gyro effect, etc.
The spin of the projectile body will also lead to the conical movement of the projectile body, and the induced resistance directly generated by it will greatly reduce the range, and even cause the flight instability of the projectile body in serious cases.The American Knight Hawk sounding rocket has shown divergent conical motion many times in the testflight testThis has also happened in.
The coupling motion of nutation and precession is the main factor that affects the stability of conical motion of rockets.On the problem of nutation stability of spin projectile, many experts and scholars have proposed a variety of modeling and analysis methods. For example, Curry WH and others have established the motion model of spin projectile only under the condition of nutation motion, and analyzed the stability of the model. On this basis, MAO Xue rui and others have given the stability critical speed and critical cone angle of spin projectile with practical examples.
Since the conical motion of a spinning projectile is a composite motion of nutation and precession, it is necessary not only to study the stability characteristics of nutation in theory, but also to study the precession characteristics under the stable conditions of nutation. Based on the means of numerical simulation, the conical motion in the experiment can be reproduced. On this basis, if the analytical solution of this phenomenon can be obtained,It is of great significance to fully understand the physical essence of the conical motion of the spinning projectile, improve the design of the control system, and improve the flight stability of the projectile.
Yan Xiaoyong[1]The conclusions are as follows:
(1) A conical motion model of spinning projectile is established, which is defined by nutation and precession variables.
(2) The chapter precession motion characteristics of the spin projectile dynamic system are analyzed analytically, and the conditions that the projectile rotational speed and Magnus torque need to meet when the system nutation is stable are obtained.
(3) It is demonstrated that the nonlinear system exists when the missile body is at the critical speedStability limit cycleIn the case of limit cycle, the analytical expression of the rotational speed of conical motion is given, and it is explained that the dynamic frequency of the system moving towards the trajectory will be related to the missile body system damping, Magnus torque and the rotational inertia of the missile body.
Instability analysis
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Almost all the last stage rockets launched by small satellites are spin stabilizedSolid rocket motorFor larger satellites, three-axis positioning is adopted.Due to the thin air in the working environment, the external force of air on the aircraft is generally ignored.The mass of the small satellite is about 50kg. If the three-axis positioning is also used or the control system is added, a relatively large negative mass will be added.
As early as the 1980s, in the process of the U.S. Star-48 rotating solid rocket motor carrying satellites, the irregular conical motion of the aircraft, that is, nutation phenomenon, was found, which was enough to lead to the failure of the launch mission.Although people have done a lot of research on this phenomenon, the Star-48 engine had to use nutation control device to prevent the nutation angle from increasing during flight, which did not fundamentally solve the problem of nutation instability.
Gao Ye et al. analyzed the nutation instability of rotating solid rocket motor by using the variable mass system method.The charge inside the engine is simplified as a grain of variable mass system. Through the analysis of the system attitude motion equation, the influence of mass change on the rotation attitude motion of the aircraft is obtained, and several typical charges are calculated and analyzed.
The results show that the disappearance of the solid charge mass has a favorable effect on the rotation movement when the end face is burnt, which makes the lateral angular velocity of the aircraft gradually stable;For tubular charge, the result is just the opposite. The disappearance of mass makes the rotating lateral angular velocity increase exponentially, which leads to the instability of the aircraft.Through the analysis of the results, the design idea of how to control the rotation nutation and stability of the engine is proposed. The analysis method can also help solve the problem of complex charge rotationSolid rocket motorNutation instability of aircraft.[2]
