CN108549787A - A kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball - Google Patents
A kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball Download PDFInfo
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Abstract
The present invention proposes a kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball, belongs to Dynamic Modeling technical field.The method is equivalent based on movement pulsation spherical model, using Newton Euler methods and functional relationship, establishes out the equivalent differential equation that can obtain storage tank stress, liquid motion and rocket attitude motion, achievees the purpose that the mechanical environment for accurately indicating liquid rocket.This method has fully considered in the case of the quick posture adjustment of rocket wide-angle in storage tank liquid substantially Nonlinear Sloshing, and consider the influence of surface tension of liquid and liquid capillary force, the precision of model is improved, can effectively solve the problems, such as that the linear equivalences such as traditional spherical pendulum or spring-mass mechanical model can not be suitable for large amplitude liquid sloshing and interfere rocket.
Description
Technical field
The present invention relates to a kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball, belong to dynamics
Modeling technique field.
Background technology
The shaking of liquid refers to liquid free surface due to the movement that is generated by external disturbance or excitation in tank.Fire
The shaking phenomenon of liquid influences the structural strength of rocket and kinetic stability very big in arrow storage tank.Especially rocket significantly
In the case of quick posture adjustment, such as rocket posture adjustment section, liquid is likely to occur very strong substantially Nonlinear Sloshing.In storage tank liquid sloshing with
Tank arrangement intercouples, and the structural strength of fuel tank can be caused by leading to the problem of larger impact force, slosh torque.On the other hand,
With the continuous development of space technology, the proportion that liquid fuel quality accounts for filled vehicle mass constantly increases, liquid sloshing and whole rocket
Influence of the coupling of structure to whole rocket attitude motion is very important.Gesture stability and orbit control accuracy of the load to rocket simultaneously
Requirement it is also higher and higher, so, storage tank liquid sloshing is must take into consideration in the design process of rocket totality and control system
It influences.
Currently, being all based on the same hypothesis greatly about the research of filling liquid rocket attitude dynamics and control：Liquid fuel shakes
Dynamic amplitude is much smaller than storage tank size, i.e., linear liquid sloshing；In this case, it is possible to linear etc. with spherical pendulum or spring-mass etc.
Mechanical model is imitated to simulate influence of the liquid sloshing to rocket.But when rocket Large Angle Rapid Maneuvering, such as rocket tune
Appearance section, liquid fuel significantly shake and cannot be applicable in；Simultaneously in this case, due to hydrokinetics calculation problem itself
Complexity and arrow carry computing resource limitation, if using be based on computational fluid dynamics (Computational fluid
Dynamics, CFD) method of model simulates liquid sloshing kinetic characteristics, and then carries out rocket just (rigid motion)-liquid
(liquid sloshing)-control (control strategy design) coupled system Study on Integration and be applied to aerospace engineering in will be it is unpractical and
It is difficult to realize.Therefore there is an urgent need for carry out the filling liquid rocket dynamics research based on large amplitude liquid sloshing Equivalent Mechanical Model.
Invention content
The technical issues of present invention for lacking based on large amplitude liquid sloshing Equivalent Mechanical Model in the prior art, it is proposed that
A kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball, the technical solution taken are as follows：
A kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball, the method for establishing model packet
It includes：
Step 1: determining rocket body coordinate system；
Step 2: i-th of tank in the rocket is equivalent to spherical storage chamber, the tank liquid is equivalent to a matter
Measure constant and radius variable uniform pulsation ball, wherein i=1,2 ..., n, for VTOL vehicle n=2；I-th
Pulsing ball can be in i-th of spherical storage intracavitary free movement, but keeps an instant contact point with spherical cavity wall always；
Step 3: according to each physical quantity that step 1 determines, in the case where not considering RCS controls, obtain without described
The Newton-Euler equations of the rocket of pulsation ball；
Step 4: obtaining adding for i-th of pulsation ball translation according to relative acceleration, the aceleration of transportation and Coriolis acceleration
Speed；
Step 5: using the acceleration and i-th of pulsation ball of described i-th pulsation ball translation relative to contact point PaiTurn
Dynamic angular speed obtains the Newton-Euler equations of i-th of pulsation ball；
Step 6: according to contact point PaiThe amplitude of the spherical storage chamber in i-th of place and the normal force of i-th of pulsation ball interaction
The energy variation amount of i-th of pulsation ball, which is equal to the width, to be determined to three performance factors of the change of the energy of i-th of pulsation ball
Value is along radial direction work done；And the amplitude is equal to along radius according to the energy variation amount of described i-th pulsation ball
Direction work done obtains the model of the amplitude；
Step 7: the model of amplitude described in step 6 to be brought into the Newton- of i-th of pulsation ball described in step 5
In Euler equations, the final kinetics equation for obtaining complete movement pulsation ball；The dynamics of the complete movement pulsation ball
Equation is the rocket large amplitude liquid sloshing model.
Further, the determination process of rocket body coordinate system described in step 1 is：By the body coordinate system of rocket
O1x1y1z1Origin O1It is defined at the rocket barycenter not comprising tank liquid.
Further, the equivalence principle of spherical storage chamber described in step 2 is：
The barycenter of spherical cavity after equivalent is overlapped with the barycenter of rocket fuel tank；
After equivalent, the barycenter of liquid can be moved in correct physical space；To the VTOL delivery in posture adjustment section
One sub- grade of device, it is equivalent after spherical cavity diameter and rocket fuel tank equal length.
Further, the Newton-Euler equations of the rocket without the pulsation ball described in step 3 are：
Wherein, vectorial upper right mark "×" indicates the antisymmetric matrix of vector；M is the rocket matter not comprising tank liquid
Amount；T indicates the time；VcFor origin O1Translational velocity under inertial system；FLiFor in contact point PaiPlace exist i-th pulsation ball with
The interaction force of i-th of spherical cavity；FEFor external force suffered by rocket；TLiFor in contact point PaiThere are i-th of pulsation balls and i-th at place
The phase separation torque of a spherical cavity；IbInertial tensor for rocket relative to barycenter；Ω is the body coordinate system O1x1y1z1
Angular speed under inertial coodinate system；rEFor radius vectors of the outer point of force application E in body coordinate system；TEFor the outer of external force suffered by rocket
Torque；rPi=RieiFor PaiRelative to CtiRadius vector, RiFor in the radius of i-th of spherical storage chamber and the geometry of the spherical storage chamber
The heart is Cti；eiFor CtiTo the barycenter S of i-th of pulsation balliRadius vector riUnit vector；rtiFor CtiArrow in body coordinate system
Diameter.
Further, in contact point PaiThere are the interaction force F of i-th pulsation ball and i-th of spherical cavity at placeLiMould
Type is：
FLi=Niei+Fbi
In contact point PaiThere are the phase separation torque T of i-th pulsation ball and i-th of spherical cavity at placeLiModel be：
TLi=15 ν msiωsiω0/(ω0-ωsi)
Wherein, FbiFor liquid friction force；NiFor contact point PaiLocate i-th of spherical cavity and ball interaction of pulsing for i-th
The amplitude of normal force, BiThe body force pulsed suffered by ball for i-th, and Fbi=cfmsiνVsi/a2, cfFor liquid and storage tank
The coefficient of sliding friction, ν are liquid motion viscosity, and a is storage tank characteristic length, msiFor the quality of i-th of pulsation ball；ω0Indicate with
I-th of pulsation relevant amount of ball initial time angular speed, ω0=1.08 ωi；ωiIndicate with respect to i-th spherical shape of i-th of pulsation ball
The angular speed of chamber.
Further, the process of acceleration that i-th of pulsation ball translation is obtained described in step 4 is：By relative acceleration,
The aceleration of transportation and Coriolis acceleration are added summation, and the acceleration of i-th of pulsation ball translation is：
ai=ari+aei+aci
Wherein,
Relative acceleration is
The aceleration of transportation isAndTo lead
The even tangential acceleration of point, Ω × [Ω × (ri+rti)] it is the method phase acceleration involved a little；
Coriolis acceleration is aci=2 Ω×Vsi；
Wherein, VsiFor speed of i-th of pulsation ball in body coordinate system；For VsiDerivative；For origin O1Used
Translational velocity V under property systemcDerivative；For the derivative of Ω；ForAntisymmetric matrix..
Further, i-th of pulsation ball of step 5 is relative to contact point PaiThe angular speed of rotation be：
Wherein,For due to i-th pulse the radius of a ball change generation Coriolis acceleration caused by
Ball pulse relative to contact point PaiAngular acceleration；ωsiFor angular speed of i-th of pulsation ball in body coordinate system；riFor arrow
Diameter riThe mould of (black matrix) is long；For ωsiDerivative；For the derivative of Ω.
Further, the Newton-Euler equations of i-th of pulsation ball described in step 5 are：
Wherein, vectorial upper right mark "×" indicates the antisymmetric matrix of vector；msiFor the quality of i-th of pulsation ball；VcFor
Origin O1Translational velocity under inertial system；FLiFor in contact point PaiThere is the mutual of pulse for i-th ball and i-th spherical cavity in place
Active force；FEFor external force suffered by rocket；TLiFor in contact point PaiThere are the phase separations of i-th pulsation ball and i-th of spherical cavity at place
Torque；IbInertial tensor for rocket relative to barycenter；Ω is the body coordinate system O1x1y1z1Angle under inertial coodinate system
Speed；rEFor radius vectors of the outer point of force application E in body coordinate system；TEFor the moment of face of external force suffered by rocket；rPi=RieiFor Pai
Relative to CtiRadius vector, RiIt is C for the radius and the spherical geometric center for storing chamber of i-th of spherical storage chamberti；eiFor CtiTo
The barycenter S of i pulsation balliRadius vector riUnit vector；rtiFor CtiRadius vector in body coordinate system；riFor radius vector riIt is (black
Body) mould it is long.
Further, the process of the model of amplitude described in step 6 includes：
The first step：Determine contact point PaiLocate the amplitude N of the normal force of i-th of spherical cavity and i-th of pulsation ball interactioni
The change of the energy of i-th of pulsation ball shows that three factors, three factors are respectively capillary potential energy PC, deformation kinetic energy Td
With angular kinetic energy TH；The capillary potential energy PC, deformation kinetic energy TdWith angular kinetic energy THModel be respectively：
Wherein, LiFor the radius of i-th of pulsation ball, H is the angular momentum of i-th of pulsation ball；
Indicate LiDerivative；σiFor the surface tension of the liquid in i-th of storage tank；
Second step：The energy variation amount that i-th of pulsation ball is obtained according to three factors described in the first step is equal to NiAlong half
Diameter direction work done；The energy variation amount of i-th of pulsation ball is equal to NiModel along radial direction work done is：
-NidLi=d (PC+Td+TH)
Third walks：The model of work(described in second step is directed to LiSecondary derivation is done, is obtainedExpression formula：
4th step：Described in third is walkedExpression formula with described i-th pulsation ball Newton-Euler equations combined,
Obtain amplitude NiModel be：
Wherein, wiAngular speed for i-th of pulsation ball barycenter relative to i-th of spherical cavity, and
Further, rocket large amplitude liquid sloshing model described in step 7 is：
Advantageous effect of the present invention：
The mould that a kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball proposed by the present invention is established
Type can be used for the large amplitude liquid sloshing model of Practical Project, based on movement pulsation spherical model, using Newton-Euler methods and
Functional relationship and the influence for considering surface tension of liquid and liquid capillary force.Obtain storage tank stress, liquid motion and rocket appearance
The equivalent differential equation of state movement.It can accurately indicate the mechanical environment of liquid rocket, and be carried for the control of liquid rocket posture adjustment section
For input, control accuracy is improved.This method has fully considered that liquid is substantially non-in storage tank in the case of the quick posture adjustment of rocket wide-angle
Linear sloshing, and consider the influence of surface tension of liquid and liquid capillary force, the precision of model is improved, can effectively solve to pass
The problem of linear equivalences such as spherical pendulum or spring-mass of system mechanical model can not interfere rocket suitable for large amplitude liquid sloshing.
Description of the drawings
Fig. 1 is the rocket equivalent model schematic diagram containing Liquid-fuel tank.
Fig. 2 is liquid stress diagram.
Specific implementation mode
With reference to specific embodiment, the present invention will be further described, but the present invention should not be limited by the examples.
Embodiment 1：
A kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball, as shown in Figure 1, by rocket ontology
Coordinate system O1x1y1z1Origin O1It is defined at the rocket barycenter not comprising tank liquid, the Rocket mass not comprising tank liquid is
M, body coordinate system O1x1y1z1Angular speed under inertial coodinate system is Ω, origin O1Translational velocity under inertial system is Vc；Fire
External force and moment of face suffered by arrow are respectively FEAnd TE, rEFor radius vectors of the outer point of force application E in body coordinate system；IbFor rocket phase
For the inertial tensor of barycenter；According to MPBM equivalent ways, the i-th (i=1,2 ..., n, for VTOL vehicle n=
2) a storage tank is equivalent to the uniform pulsation ball of i-th spherical spherical cavity and i-th of radius variable mass conservation；I-th of pulsation ball
Can the free movement in i-th of spherical cavity, but always with spherical cavity wall keep an instant contact point, contact point Pai, also known as
Pressure spot, and in point PaiThere are the interaction force F of i-th pulsation ball and i-th of spherical cavity at placeLiWith opplied moment TLi；I-th
The radius of a spherical cavity is Ri, and its geometric center is Cti；The quality of i-th of pulsation ball is msi, barycenter Si, relative to Si
Inertial tensor be Isi, angular speed and speed in body coordinate system are respectively ωsiAnd vsi；CtiAnd SiIn ontology coordinate
Radius vector in system is respectively rtiAnd rsi, CtiTo SiRadius vector be ri, and eiAnd riRespectively riUnit vector and mould it is long；rPi=
RieiFor PaiRelative to CtiRadius vector.
The method for establishing model includes：
Step 1: determining rocket body coordinate system；
Step 2: i-th of tank in the rocket is equivalent to spherical storage chamber, the tank liquid is equivalent to a matter
Measure constant and radius variable uniform pulsation ball, wherein i=1,2 ..., n, for VTOL vehicle n=2；I-th
Pulsing ball can be in i-th of spherical storage intracavitary free movement, but keeps an instant contact point with spherical cavity wall always；
Step 3: according to each physical quantity that step 1 determines, in the case where not considering RCS controls, obtain without described
The Newton-Euler equations of the rocket of pulsation ball；
Step 4: obtaining adding for i-th of pulsation ball translation according to relative acceleration, the aceleration of transportation and Coriolis acceleration
Speed；
Step 5: using the acceleration and i-th of pulsation ball of described i-th pulsation ball translation relative to contact point PaiTurn
Dynamic angular speed obtains the Newton-Euler equations of i-th of pulsation ball；
Step 6: according to contact point PaiThe amplitude of the spherical storage chamber in i-th of place and the normal force of i-th of pulsation ball interaction
The energy variation amount of i-th of pulsation ball, which is equal to the width, to be determined to three performance factors of the change of the energy of i-th of pulsation ball
Value is along radial direction work done；And the amplitude is equal to along radius according to the energy variation amount of described i-th pulsation ball
Direction work done obtains the model of the amplitude；
Step 7: the model of amplitude described in step 6 to be brought into the Newton- of i-th of pulsation ball described in step 5
In Euler equations, the final kinetics equation for obtaining complete movement pulsation ball；The dynamics of the complete movement pulsation ball
Equation is the rocket large amplitude liquid sloshing model.The rocket large amplitude liquid sloshing model is：
Wherein, the determination process of rocket body coordinate system described in step 1 is：By the body coordinate system O of rocket1x1y1z1It is former
Point O1It is defined at the rocket barycenter not comprising tank liquid.
The equivalence principle of spherical storage chamber described in step 2 is：
(1) barycenter of the spherical cavity after equivalent is overlapped with the barycenter of rocket fuel tank；
(2) after equivalent, the barycenter of liquid can be moved in correct physical space；To the VTOL fortune in posture adjustment section
Carry one sub- grade of device, it is equivalent after spherical cavity diameter and rocket fuel tank equal length.
The Newton-Euler equations of rocket without the pulsation ball described in step 3 are：
Wherein, vectorial upper right mark "×" indicates the antisymmetric matrix of vector；M is the rocket matter not comprising tank liquid
Amount；T indicates the time；VcFor origin O1Translational velocity under inertial system；FLiFor in contact point PaiPlace exist i-th pulsation ball with
The interaction force of i-th of spherical cavity；FEFor external force suffered by rocket；TLiFor in contact point PaiThere are i-th of pulsation balls and i-th at place
The phase separation torque of a spherical cavity；IbInertial tensor for rocket relative to barycenter；Ω is the body coordinate system O1x1y1z1
Angular speed under inertial coodinate system；rEFor radius vectors of the outer point of force application E in body coordinate system；TEFor the outer of external force suffered by rocket
Torque；rPi=RieiFor PaiRelative to CtiRadius vector, RiFor in the radius of i-th of spherical storage chamber and the geometry of the spherical storage chamber
The heart is Cti；eiFor CtiTo the barycenter S of i-th of pulsation balliRadius vector riUnit vector；rtiFor CtiArrow in body coordinate system
Diameter.
In contact point PaiThere are the interaction force F of i-th pulsation ball and i-th of spherical cavity at placeLiModel be：
FLi=Niei+Fbi
In contact point PaiThere are the phase separation torque T of i-th pulsation ball and i-th of spherical cavity at placeLiModel be：
TLi=15 ν msiωsiω0/(ω0-ωsi)
Wherein, FbiFor liquid friction force；NiFor contact point PaiLocate i-th of spherical cavity and ball interaction of pulsing for i-th
The amplitude of normal force, BiThe body force pulsed suffered by ball for i-th, and Fbi=cfmsiνVsi/a2, cfFor liquid and storage tank
The coefficient of sliding friction, ν are liquid motion viscosity, and a is storage tank characteristic length, msiFor the quality of i-th of pulsation ball；ω0Indicate with
I-th of pulsation relevant amount of ball initial time angular speed, ω0=1.08 ωi；ωiIndicate with respect to i-th spherical shape of i-th of pulsation ball
The angular speed of chamber.
The process of acceleration that i-th of pulsation ball translation is obtained described in step 4 is：By relative acceleration, the aceleration of transportation
And Coriolis acceleration is added summation, the acceleration of i-th of pulsation ball translation is：
ai=ari+aei+aci
Wherein,
Relative acceleration is
The aceleration of transportation isAndTo lead
The even tangential acceleration of point, Ω × [Ω × (ri+rti)] it is the method phase acceleration involved a little；
Coriolis acceleration is aci=2 Ω×Vsi；
Wherein, VsiFor speed of i-th of pulsation ball in body coordinate system；For VsiDerivative；For origin O1Used
Translational velocity V under property systemcDerivative；For the derivative of Ω；ForAntisymmetric matrix.
I-th of pulsation ball of step 5 is relative to contact point PaiThe angular speed of rotation be：
Wherein,For due to i-th pulse the radius of a ball change generation Coriolis acceleration caused by
Ball pulse relative to contact point PaiAngular acceleration；ωsiFor angular speed of i-th of pulsation ball in body coordinate system；riFor arrow
Diameter riThe mould of (black matrix) is long；For ωsiDerivative；For the derivative of Ω.
Described in step 5 i-th pulsation ball Newton-Euler equations be：
Wherein, vectorial upper right mark "×" indicates the antisymmetric matrix of vector；msiFor the quality of i-th of pulsation ball；VcFor
Origin O1Translational velocity under inertial system；FLiFor in contact point PaiThere is the mutual of pulse for i-th ball and i-th spherical cavity in place
Active force；FEFor external force suffered by rocket；TLiFor in contact point PaiThere are the phase separations of i-th pulsation ball and i-th of spherical cavity at place
Torque；IbInertial tensor for rocket relative to barycenter；Ω is the body coordinate system O1x1y1z1Angle under inertial coodinate system
Speed；rEFor radius vectors of the outer point of force application E in body coordinate system；TEFor the moment of face of external force suffered by rocket；rPi=RieiFor Pai
Relative to CtiRadius vector, RiIt is C for the radius and the spherical geometric center for storing chamber of i-th of spherical storage chamberti；eiFor CtiTo
The barycenter S of i pulsation balliRadius vector riUnit vector；rtiFor CtiRadius vector in body coordinate system；riFor radius vector riIt is (black
Body) mould it is long.Also, the Newton-Euler equations of simultaneous formula rocket are needed when numerical computations and ball of pulsing for i-th
Newton-Euler equations, and the coupling terms in the two formulas are also rocket rigid body-liquid fuel Dynamics Coupling feature
It embodies.
The process of the model of amplitude described in step 6 includes：
The first step：Determine contact point PaiLocate the amplitude N of the normal force of i-th of spherical cavity and i-th of pulsation ball interactioni
The change of the energy of i-th of pulsation ball shows that three factors, three factors are respectively capillary potential energy PC, deformation kinetic energy Td
With angular kinetic energy TH；The capillary potential energy PC, deformation kinetic energy TdWith angular kinetic energy THModel be respectively：
Wherein, LiAnd Li,minRadius (the i.e. R of respectively i-th pulsation balli-ri) and least radius；H is i-th of pulsation ball
Angular momentum； Indicate LiDerivative；σiFor the table of the liquid in i-th of storage tank
Face tension；
Second step：The energy variation amount that i-th of pulsation ball is obtained according to three factors described in the first step is equal to NiAlong half
Diameter direction work done；The energy variation amount of i-th of pulsation ball is equal to NiModel along radial direction work done is：
-NidLi=d (PC+Td+TH)
Third walks：The model of work(described in second step is directed to LiSecondary derivation is done, is obtainedExpression formula：
4th step：Described in third is walkedExpression formula with described i-th pulsation ball Newton-Euler equations combined,
Obtain amplitude NiModel be：
Wherein, wiAngular speed for i-th of pulsation ball barycenter relative to i-th of spherical cavity, and
Although the present invention is disclosed as above with preferred embodiment, it is not limited to the present invention, any to be familiar with this
The people of technology can do various changes and modification, therefore the protection of the present invention without departing from the spirit and scope of the present invention
Range should be subject to what claims were defined.
Claims (10)
1. a kind of rocket large amplitude liquid sloshing method for establishing model based on movement pulsation ball, which is characterized in that the model is built
Cube method includes：
Step 1: determining rocket body coordinate system；
Step 2: i-th of tank in the rocket is equivalent to spherical storage chamber, the tank liquid is equivalent to a quality not
Become and the uniform pulsation ball of radius variable, wherein i=1,2 ..., n, for VTOL vehicle n=2；I-th of pulsation
Ball can be in i-th of spherical storage intracavitary free movement, but keeps an instant contact point with spherical cavity wall always；
Step 3: according to each physical quantity that step 1 determines, in the case where not considering RCS controls, obtains and be free of the pulsation
The Newton-Euler equations of the rocket of ball；
Step 4: obtaining the acceleration of i-th of pulsation ball translation according to relative acceleration, the aceleration of transportation and Coriolis acceleration
Degree；
Step 5: using the acceleration and i-th of pulsation ball of described i-th pulsation ball translation relative to contact point PaiRotation
Angular speed obtains the Newton-Euler equations of i-th of pulsation ball；
Step 6: according to contact point PaiThe amplitude pair of the spherical storage chamber in i-th of place and the normal force of i-th of pulsation ball interaction the
Three performance factors of the change of the energy of i pulsation ball determine that the energy variation amount of i-th of pulsation ball is equal to the amplitude edge
Radial direction work done；And the amplitude is equal to along radial direction according to the energy variation amount of described i-th pulsation ball
Work done obtains the model of the amplitude；
Step 7: the model of amplitude described in step 6 to be brought into the side Newton-Euler of i-th of pulsation ball described in step 5
Cheng Zhong, the final kinetics equation for obtaining complete movement pulsation ball；It is described it is complete movement pulsation ball kinetics equation be
For the rocket large amplitude liquid sloshing model.
2. method according to claim 1, which is characterized in that the determination process of rocket body coordinate system described in step 1 is：
By the body coordinate system O of rocket1x1y1z1Origin O1It is defined at the rocket barycenter not comprising tank liquid.
3. method according to claim 1, which is characterized in that the equivalence principle of spherical storage chamber described in step 2 is：
The barycenter of spherical cavity after equivalent is overlapped with the barycenter of rocket fuel tank；
After equivalent, the barycenter of liquid can be moved in correct physical space；To the VTOL vehicle one in posture adjustment section
Sub- grade, it is equivalent after spherical cavity diameter and rocket fuel tank equal length.
4. method according to claim 1, which is characterized in that be free of the rocket of the pulsation ball described in step 3
Newton-Euler equations are：
Wherein, vectorial upper right mark "×" indicates the antisymmetric matrix of vector；M is the Rocket mass not comprising tank liquid；T tables
Show the time；VcFor origin O1Translational velocity under inertial system；FLiFor in contact point PaiThere are i-th of pulsation ball and i-th at place
The interaction force of spherical cavity；FEFor external force suffered by rocket；TLiFor in contact point PaiThere are i-th of pulsation ball and i-th of balls at place
The phase separation torque of shape chamber；IbInertial tensor for rocket relative to barycenter；Ω is the body coordinate system O1x1y1z1In inertia
Angular speed under coordinate system；rEFor radius vectors of the outer point of force application E in body coordinate system；TEFor the moment of face of external force suffered by rocket；
rPi=RieiFor PaiRelative to CtiRadius vector, RiIt is for the radius and the spherical geometric center for storing chamber of i-th of spherical storage chamber
Cti；eiFor CtiTo the barycenter S of i-th of pulsation balliRadius vector riUnit vector；rtiFor CtiRadius vector in body coordinate system.
5. method according to claim 4, which is characterized in that in contact point PaiThere are i-th of pulsation ball and i-th are spherical at place
The interaction force F of chamberLiModel be：
FLi=Niei+Fbi
In contact point PaiThere are the phase separation torque T of i-th pulsation ball and i-th of spherical cavity at placeLiModel be：
TLi=15 ν msiωsiω0/(ω0-ωsi)
Wherein, FbiFor liquid friction force；NiFor contact point PaiLocate the normal direction of i-th of spherical cavity and i-th of pulsation ball interaction
The amplitude of power, BiThe body force pulsed suffered by ball for i-th, and Fbi=cfmsiνVsi/a2, cfFor the sliding of liquid and storage tank
Friction coefficient, ν are liquid motion viscosity, and a is storage tank characteristic length, msiFor the quality of i-th of pulsation ball；ω0It indicates and i-th
The pulsation relevant amount of ball initial time angular speed, ω0=1.08 ωi；ωiIndicate i-th of pulsation ball with respect to i-th spherical cavity
Angular speed.
6. method according to claim 1, which is characterized in that obtain the acceleration of i-th of pulsation ball translation described in step 4
Process be：Relative acceleration, the aceleration of transportation and Coriolis acceleration are added and summed, i-th of pulsation ball translation
Acceleration is：
ai=ari+aei+aci
Wherein,
Relative acceleration is
The aceleration of transportation isAndTo involve a little
Tangential acceleration, Ω×[Ω×(ri+rti)] it is the method phase acceleration involved a little；
Coriolis acceleration is aci=2 Ω×Vsi；
Wherein, VsiFor speed of i-th of pulsation ball in body coordinate system；For VsiDerivative；For origin O1In inertial system
Under translational velocity VcDerivative；For the derivative of Ω；ForAntisymmetric matrix.
7. method according to claim 1, which is characterized in that i-th of pulsation ball of step 5 is relative to contact point PaiRotation
Angular speed be：
Wherein,For due to i-th pulse the radius of a ball change generation Coriolis acceleration caused by pulse
Ball is relative to contact point PaiAngular acceleration；ωsiFor angular speed of i-th of pulsation ball in body coordinate system；riFor radius vector ri
Mould it is long；For ωsiDerivative；For the derivative of Ω.
8. method according to claim 1, which is characterized in that the side Newton-Euler of i-th of pulsation ball described in step 5
Cheng Wei：
Wherein, vectorial upper right mark "×" indicates the antisymmetric matrix of vector；msiFor the quality of i-th of pulsation ball；VcFor origin O1
Translational velocity under inertial system；FLiFor in contact point PaiThere are the interactions of i-th pulsation ball and i-th of spherical cavity at place
Power；FEFor external force suffered by rocket；TLiFor in contact point PaiThere are the phase separation torques of i-th pulsation ball and i-th of spherical cavity at place；
IbInertial tensor for rocket relative to barycenter；Ω is the body coordinate system O1x1y1z1Angular speed under inertial coodinate system；
rEFor radius vectors of the outer point of force application E in body coordinate system；TEFor the moment of face of external force suffered by rocket；rPi=RieiFor PaiRelatively
In CtiRadius vector, RiIt is C for the radius and the spherical geometric center for storing chamber of i-th of spherical storage chamberti；eiFor CtiTo i-th
The barycenter S of pulsation balliRadius vector riUnit vector；rtiFor CtiRadius vector in body coordinate system；riFor radius vector riMould it is long.
9. method according to claim 1, which is characterized in that the process of the model of amplitude described in step 6 includes：
The first step：Determine contact point PaiLocate the amplitude N of the normal force of i-th of spherical cavity and i-th of pulsation ball interactioniI-th
The change of the energy of a pulsation ball shows that three factors, three factors are respectively capillary potential energy PC, deformation kinetic energy TdThe angle and
Kinetic energy TH；The capillary potential energy PC, deformation kinetic energy TdWith angular kinetic energy THModel be respectively：
Wherein, LiFor the radius of i-th of pulsation ball, H is the angular momentum of i-th of pulsation ball；
Indicate LiDerivative；σiFor the surface tension of the liquid in i-th of storage tank；
Second step：The energy variation amount that i-th of pulsation ball is obtained according to three factors described in the first step is equal to NiAlong radial direction
Work done；The energy variation amount of i-th of pulsation ball is equal to NiModel along radial direction work done is：
-NidLi=d (PC+Td+TH)
Third walks：The model of work(described in second step is directed to LiSecondary derivation is done, is obtainedExpression formula：
4th step：Described in third is walkedExpression formula with described i-th pulsation ball Newton-Euler equations is combined, acquisition
Amplitude NiModel be：
Wherein, wiAngular speed for i-th of pulsation ball barycenter relative to i-th of spherical cavity, and
10. method according to claim 1, which is characterized in that rocket large amplitude liquid sloshing model described in step 7 is：
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