CN113987894A - Unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions - Google Patents

Unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions Download PDF

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CN113987894A
CN113987894A CN202111637133.6A CN202111637133A CN113987894A CN 113987894 A CN113987894 A CN 113987894A CN 202111637133 A CN202111637133 A CN 202111637133A CN 113987894 A CN113987894 A CN 113987894A
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李道春
赵仕伟
邵浩原
阚梓
姚卓尔
申童
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Abstract

The invention discloses an unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions, which comprises the steps of calculating the pneumatic derivative of an unmanned aerial vehicle considering rainfall influence and the force and moment generated in the raindrop impact process through fluid mechanics simulation, and establishing a small disturbance linear equation of an unmanned aerial vehicle flexible flight dynamics model considering the rainfall influence by combining an elastic motion equation and an unmanned aerial vehicle rigid flight mechanics model; the unmanned aerial vehicle dynamics modeling under the rainfall condition is completed on the basis of a small disturbance linear equation of the unmanned aerial vehicle flexible flight dynamics model considering the rainfall influence. The method can effectively obtain the flight performance condition of the unmanned aerial vehicle in the rainfall weather, thereby providing guidance thought for related design and improving all-weather flight capability of the unmanned aerial vehicle.

Description

Unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions
Technical Field
The invention belongs to the technical field of unmanned aerial vehicles, and particularly relates to an unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions, which can be used for unmanned aerial vehicle dynamics modeling under the rainfall weather conditions.
Background
The ultra-long time-of-flight unmanned aerial vehicle has important application value and development potential due to the fact that the ultra-long time-of-flight unmanned aerial vehicle can execute important tasks. However, in the face of harsh flight mission requirements, innovative design solutions cause new problems while applying new technologies to expand the design space. These new problems are mainly manifested in structural nonlinearity, aerodynamic nonlinearity and the coupling problem of structural elastic motion and all-machine rigid motion. The design of the ultra-long unmanned aerial vehicle during navigation leads to the sharp increase of the flexibility of the aircraft and easy generation of rigid and elastic coupling phenomena due to the fact that the unmanned aerial vehicle has a large wingspan and needs to use a large number of light structures, and therefore structural damage or stalling is caused.
When flying under the rainfall condition, the unmanned aerial vehicle can have great influence on the flight performance of the unmanned aerial vehicle, including the aerodynamic performance of each control surface, each wing and each empennage, so that the stability and maneuverability of the flying are deteriorated, the flying resistance is increased, the lift force is reduced, and the all-weather flying capacity of the unmanned aerial vehicle during long-term flight can be seriously influenced. Therefore, in order to cope with the environment, the influence on the flight capability of the unmanned aerial vehicle under the weather condition must be known and understood, and the adaptability of the unmanned aerial vehicle under the weather condition is improved, so that the all-weather flight capability of the unmanned aerial vehicle is improved.
Disclosure of Invention
The invention provides an unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions aiming at improving all-weather flight capability of an unmanned aerial vehicle, and an unmanned aerial vehicle flight dynamics model is established by calculating rainfall parameters and calculating impact force and impact moment generated by raindrops.
The specific technical scheme is as follows: an unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions comprises the following steps:
s100, calculating an impact force and an impact moment generated when the unmanned aerial vehicle pneumatic coefficient, the pneumatic derivative and raindrops impact the airplane based on the rainfall weather condition through hydrodynamics simulation;
s200, expressing the aerodynamic coefficient and the aerodynamic derivative of the unmanned aerial vehicle based on the rainfall weather condition, and the impact force and the impact moment generated when raindrops impact the airplane in an initial balance equation of the unmanned aerial vehicle, and establishing a rigid unmanned aerial vehicle flight dynamics model based on the rainfall weather condition according to the initial balance equation of the unmanned aerial vehicle;
s300, considering the flexibility of the wings of the unmanned aerial vehicle, establishing a finite element model of the wings, establishing an elastic motion equation on the basis, and reducing the elastic motion equation;
s400, establishing an unmanned aerial vehicle flexible flight dynamics model considering rainfall influence by combining an elastic motion equation and a rigid unmanned aerial vehicle flight dynamics model;
s500, establishing a small disturbance linear equation of the flexible flight dynamics model of the unmanned aerial vehicle considering rainfall influence on the basis of the flexible flight dynamics model of the unmanned aerial vehicle considering rainfall influence;
and S600, completing unmanned aerial vehicle dynamics modeling under the rainfall weather condition on the basis of a flexible flight dynamics small disturbance linear equation of the unmanned aerial vehicle considering rainfall influence.
Further, step S100 further includes the steps of:
and step S110, calculating the liquid water content in the air according to the rainfall rate.
Step S120, according to the liquid water content in the airLWCEstablishing an air model as a continuous phase and a raindrop model as a discrete phase, performing unsteady forced oscillation motion on the aircraft by adopting a dynamic grid to perform fluid mechanics simulation, and calculating the impact force generated when raindrops impact the aircraftImpact moment and aerodynamic coefficient; and meanwhile, evaluating the dynamic pneumatic performance of the unmanned aerial vehicle, and calculating the pneumatic derivative of the unmanned aerial vehicle.
Further, the liquid water content in the airLWCThe calculation formula of (a) is as follows:
Figure 6965DEST_PATH_IMAGE001
wherein the content of the first and second substances,ρ w is the rainwater density;Ris the rainfall rate, unit: mm/h;
Figure 337453DEST_PATH_IMAGE002
。
further, the rigid flight dynamics of the drone based on consideration of the effects of rainfall are as follows:
Figure 329679DEST_PATH_IMAGE003
wherein
Figure 352999DEST_PATH_IMAGE004
Is the coordinate of the mass center,
Figure 594625DEST_PATH_IMAGE005
is the angular velocity of the center of mass,
Figure 604169DEST_PATH_IMAGE006
is the speed of the mass center,
Figure 77001DEST_PATH_IMAGE007
as an external force, the pressure of the liquid is,
Figure 881009DEST_PATH_IMAGE008
the moment is the external moment,
Figure 875510DEST_PATH_IMAGE009
in order to be an external force caused by rainfall,
Figure 547799DEST_PATH_IMAGE010
in order to generate an external moment caused by rainfall,
Figure 514618DEST_PATH_IMAGE011
is a yaw angle, a pitch angle and a roll angle,
Figure 348582DEST_PATH_IMAGE012
is the moment of inertia of the aircraft about the coordinate axes.
Furthermore, based on the modal coordinates, the elastic motion equation is reduced by a modal truncation method, the expression of the elastic motion equation after the reduction is as follows,
Figure 33641DEST_PATH_IMAGE013
wherein
Figure 181726DEST_PATH_IMAGE014
Is a matrix of the quality of the system,
Figure 127685DEST_PATH_IMAGE015
is a matrix of the damping of the system,
Figure 273496DEST_PATH_IMAGE016
is a matrix of the stiffness of the system,
Figure 803441DEST_PATH_IMAGE017
、
Figure 692899DEST_PATH_IMAGE018
、
Figure 431048DEST_PATH_IMAGE019
respectively represents the displacement, the speed and the acceleration of the system,
Figure 606815DEST_PATH_IMAGE020
a generalized force matrix.
Further, the flexible flight dynamics model of the unmanned aerial vehicle considering the influence of rainfall is as follows:
Figure 887DEST_PATH_IMAGE021
wherein
Figure 818670DEST_PATH_IMAGE022
Is the coordinate of the mass center,
Figure 411326DEST_PATH_IMAGE023
is the angular velocity of the center of mass,
Figure 164518DEST_PATH_IMAGE024
is the speed of the mass center,
Figure 904941DEST_PATH_IMAGE025
as an external force, the pressure of the liquid is,
Figure 136202DEST_PATH_IMAGE026
the moment is the external moment,
Figure 583364DEST_PATH_IMAGE027
in order to be an external force caused by rainfall,
Figure 133556DEST_PATH_IMAGE028
in order to generate an external moment caused by rainfall,
Figure 236641DEST_PATH_IMAGE029
is a yaw angle, a pitch angle and a roll angle,
Figure 396227DEST_PATH_IMAGE030
moment of inertia of the aircraft about a coordinate axis; wherein
Figure 901158DEST_PATH_IMAGE031
Is a matrix of the quality of the system,
Figure 792891DEST_PATH_IMAGE032
is a matrix of the damping of the system,
Figure 773485DEST_PATH_IMAGE033
is a matrix of the stiffness of the system,
Figure 80970DEST_PATH_IMAGE020
in the form of a generalized force matrix,
Figure 502724DEST_PATH_IMAGE017
、
Figure 893254DEST_PATH_IMAGE018
、
Figure 705352DEST_PATH_IMAGE019
respectively representing the system displacement, velocity, acceleration.
The beneficial effects of the invention are as follows: the influence of rainfall weather conditions and aircraft flexibility on the flight dynamics of the unmanned aerial vehicle is considered, the adaptability of the unmanned aerial vehicle under the rainfall weather conditions during long-endurance is improved, and the all-weather flight capability of the unmanned aerial vehicle during long-endurance is improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a pitch angle response curve of the flexible aircraft after the unit angle of the elevator is deflected in the forward direction under different rainfall according to the embodiment.
Detailed Description
The method for modeling flight dynamics in consideration of rainfall weather according to the present invention will be described in further detail with reference to the accompanying drawings and examples.
An unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions comprises the following steps:
step S100, calculating an impact force and an impact moment generated when the unmanned aerial vehicle pneumatic coefficient, the pneumatic derivative and raindrops impact the airplane based on the rainfall weather condition through hydrodynamics simulation.
And step S110, calculating the liquid water content in the air according to the rainfall rate.
The rainfall rate is the rainfall in unit time, the rainfall rate can reflect the severity of rainfall,
the calculation formula of the liquid water content LWC in air is as follows:
Figure 970855DEST_PATH_IMAGE001
wherein the content of the first and second substances,ρ w is the rainwater density;Ris the rainfall rate, unit: mm/h;
Figure 450378DEST_PATH_IMAGE034
。
step S120, according to the liquid water content in the airLWCThe raindrops are large relative to air molecules and impact the unmanned aerial vehicle in a particle form, so that a model of the raindrops is established as a discrete phase for describing particles, air uniformly exists around the unmanned aerial vehicle, the model of the raindrops is established as a continuous phase, the dynamic grid is adopted to carry out unsteady forced oscillation motion on the aircraft for hydromechanical simulation, and the impact force, the impact moment and the pneumatic coefficient generated when the raindrops impact the aircraft are calculated; and meanwhile, evaluating the dynamic pneumatic performance of the unmanned aerial vehicle, and calculating the pneumatic derivative of the unmanned aerial vehicle.
The computational fluid dynamics software adopts software such as fluent and openfoam to establish an air model as a continuous phase and a raindrop model as a discrete phase, and adopts a dynamic grid to carry out unsteady forced oscillation motion on the aircraft for fluid mechanics simulation, so that the dynamic pneumatic performance of the unmanned aerial vehicle is evaluated, and the pneumatic derivative of the unmanned aerial vehicle is calculated.
S200, expressing the aerodynamic coefficient and the aerodynamic derivative of the unmanned aerial vehicle considering the rainfall weather conditions, and the impact force and the impact moment generated when raindrops impact the plane in an initial balance equation of the unmanned aerial vehicle, and establishing a rigid unmanned aerial vehicle flight dynamics model based on the rainfall weather conditions according to the initial balance equation of the unmanned aerial vehicle, wherein the rigid unmanned aerial vehicle flight dynamics model considering the rainfall influence is as follows:
(1) an aircraft equation of motion describing changes in position and attitude of an aircraft space;
Figure 683913DEST_PATH_IMAGE035
(2) a kinetic equation describing the motion and rotation of the aircraft's center of mass;
Figure 107941DEST_PATH_IMAGE036
wherein
Figure 22807DEST_PATH_IMAGE004
Is the coordinate of the mass center,
Figure 419154DEST_PATH_IMAGE005
is the angular velocity of the center of mass,
Figure 151486DEST_PATH_IMAGE006
is the speed of the mass center,
Figure 203756DEST_PATH_IMAGE007
as an external force, the pressure of the liquid is,
Figure 46947DEST_PATH_IMAGE008
the moment is the external moment,
Figure 235483DEST_PATH_IMAGE009
in order to be an external force caused by rainfall,
Figure 640182DEST_PATH_IMAGE010
in order to generate an external moment caused by rainfall,
Figure 976485DEST_PATH_IMAGE011
is a yaw angle, a pitch angle and a roll angle,
Figure 498733DEST_PATH_IMAGE012
is the moment of inertia of the aircraft about the coordinate axes.
Step S300, considering the flexibility of the wings of the unmanned aerial vehicle, establishing a finite element model of the wings, establishing an elastic motion equation on the basis, obtaining the modes of the wings through mode analysis, and reducing the elastic motion equation by adopting a mode truncation method.
Based on the modal coordinates, reducing the elastic motion equation by a modal truncation method, wherein the expression of the elastic motion equation after reduction is as follows,
Figure 666409DEST_PATH_IMAGE037
wherein
Figure 615911DEST_PATH_IMAGE014
Is a matrix of the quality of the system,
Figure 173931DEST_PATH_IMAGE015
is a matrix of the damping of the system,
Figure 624504DEST_PATH_IMAGE016
is a matrix of the stiffness of the system,
Figure 522053DEST_PATH_IMAGE017
、
Figure 767089DEST_PATH_IMAGE018
、
Figure 77985DEST_PATH_IMAGE019
respectively represents the displacement, the speed and the acceleration of the system,
Figure 942036DEST_PATH_IMAGE020
a generalized force matrix. For the flight dynamics analysis, only the lowest several-order modes are generally concerned, so that the order of the elastic motion equation can be reduced, and the calculation efficiency is greatly improved.
Step S400, combining an elastic motion equation and a rigid unmanned aerial vehicle flight mechanics model, establishing an unmanned aerial vehicle flexible flight dynamics model considering rainfall influence, wherein the flexible unmanned aerial vehicle is an unmanned aerial vehicle considering structural modal influence, and the unmanned aerial vehicle flexible flight dynamics model considering rainfall influence is as follows:
(1) an aircraft equation of motion describing changes in position and attitude of an aircraft space;
Figure 582839DEST_PATH_IMAGE038
(2) a kinetic equation describing the motion and rotation of the aircraft's center of mass;
Figure 874143DEST_PATH_IMAGE039
(3) describing the flexibility of the wings of the unmanned aerial vehicle based on the reduced elastic motion equation obtained by a modal truncation method;
Figure 734652DEST_PATH_IMAGE040
wherein
Figure 933552DEST_PATH_IMAGE041
Is the coordinate of the mass center,
Figure 71273DEST_PATH_IMAGE023
is the angular velocity of the center of mass,
Figure 658112DEST_PATH_IMAGE024
is the speed of the mass center,
Figure 615703DEST_PATH_IMAGE025
as an external force, the pressure of the liquid is,
Figure 883874DEST_PATH_IMAGE042
the moment is the external moment,
Figure 734DEST_PATH_IMAGE027
in order to be an external force caused by rainfall,
Figure 368262DEST_PATH_IMAGE043
in order to generate an external moment caused by rainfall,
Figure 704827DEST_PATH_IMAGE044
is a yaw angle, a pitch angle and a roll angle,
Figure 511109DEST_PATH_IMAGE045
moment of inertia of the aircraft about a coordinate axis; wherein
Figure 357843DEST_PATH_IMAGE031
Is a matrix of the quality of the system,
Figure 286484DEST_PATH_IMAGE046
is a matrix of the damping of the system,
Figure 218668DEST_PATH_IMAGE033
is a matrix of the stiffness of the system,
Figure 156537DEST_PATH_IMAGE020
in the form of a generalized force matrix,
Figure 920094DEST_PATH_IMAGE017
、
Figure 629424DEST_PATH_IMAGE018
、
Figure 439117DEST_PATH_IMAGE019
respectively representing the system displacement, velocity, acceleration.
Step S500, on the basis of the flexible flight dynamics model of the unmanned aerial vehicle considering rainfall influence, establishing a small disturbance linear equation of the flexible flight dynamics model of the unmanned aerial vehicle considering rainfall influence, writing the small disturbance linear equation into a state space form, and bringing the state space form into a pneumatic derivative, so that the small disturbance linear equation of the flexible flight dynamics model of the unmanned aerial vehicle considering rainfall influence can be obtained:
Figure 587202DEST_PATH_IMAGE047
wherein
Figure 408527DEST_PATH_IMAGE048
Is the derivative of the state variable and is,Ain the form of a matrix of states,Bis a control matrix;
the state variable of the longitudinal system of equations is
Figure 177507DEST_PATH_IMAGE049
(ii) a The controlled variable is
Figure 818703DEST_PATH_IMAGE050
。
And S600, finishing the dynamics modeling of the unmanned aerial vehicle under the rainfall weather condition on the basis of a small disturbance linear equation of the flexible flight dynamics model of the unmanned aerial vehicle considering the rainfall influence.
The invention is further described below in conjunction with the appended drawings and specific embodiments, it being understood that the embodiments described below are intended to facilitate an understanding of the invention and are not intended to be limiting in any way.
Example 1: when flying in the rainfall, the raindrop can form an additional water film on the unmanned aerial vehicle surface after striking unmanned aerial vehicle, and the water film can change the roughness on aircraft surface, leads to the great change of aerodynamic force that the aircraft received to take place. The lift coefficient can be reduced by 13 percent originally in the environment with the rainfall rate of 80mm/h, the drag coefficient can be increased by 0.0031, the lift coefficient can be reduced by 9 percent originally in the environment with the rainfall rate of 70mm/h, the drag coefficient can be increased by 0.0023, the lift coefficient can be reduced by 5 percent originally in the environment with the rainfall rate of 60mm/h, and the drag coefficient can be increased by 0.0016.
The pitch angle of the aircraft was calculated when the rainfall rate was 60mm/h, 70mm/h and 80mm/h, respectively, as shown in fig. 2. After the elevator is positively deflected, the attack angle of the unmanned aerial vehicle under normal flight conditions and at a rainfall rate of 60mm/h is slightly increased, the flight speed is reduced, so that a normal flat flight state is maintained, under the rainfall rate conditions of 70mm/h and 80mm/h, the unmanned aerial vehicle raises at the initial input stage due to the influence of raindrop impact force and moment, and the attack angle is reduced after a period of time, which indicates that the operation of the elevator is not enough to overcome the gliding tendency of the raindrop impact force and moment on the aircraft. When the airplane encounters rainfall, a low head moment is generated, and the airplane needs to improve the lift force and maintain level flight by increasing the flight speed. The result shows that when the rainfall rate is less than 70mm/h, the influence brought by raindrops can be overcome, the pitching angle of the unmanned aerial vehicle is less than 0 when the rainfall rate is more than 70mm/h, namely, the unmanned aerial vehicle has the head-lowering phenomenon, so that the problem of inevitable operation of the unmanned aerial vehicle is caused.
It will be apparent to those skilled in the art that various modifications and improvements can be made to the embodiments of the present invention without departing from the inventive concept thereof, and these modifications and improvements are intended to be within the scope of the invention.

Claims (6)

1. An unmanned aerial vehicle dynamics modeling method based on rainfall weather conditions is characterized by comprising the following steps:
s100, calculating an impact force and an impact moment generated when the unmanned aerial vehicle pneumatic coefficient, the pneumatic derivative and raindrops impact the airplane based on the rainfall weather condition through hydrodynamics simulation;
s200, expressing the aerodynamic coefficient and the aerodynamic derivative of the unmanned aerial vehicle based on the rainfall weather condition, and the impact force and the impact moment generated when raindrops impact the plane in an initial balance equation of the unmanned aerial vehicle, and establishing an unmanned aerial vehicle rigid flight dynamics model considering rainfall influence according to the initial balance equation of the unmanned aerial vehicle;
s300, considering the flexibility of the wings of the unmanned aerial vehicle, establishing a finite element model of the wings, establishing an elastic motion equation on the basis, and reducing the elastic motion equation;
s400, establishing an unmanned aerial vehicle flexible flight dynamics model considering rainfall influence by combining an elastic motion equation and a rigid unmanned aerial vehicle flight dynamics model;
s500, establishing a small disturbance linear equation of the flexible flight dynamics model of the unmanned aerial vehicle considering rainfall influence on the basis of the flexible flight dynamics model of the unmanned aerial vehicle considering rainfall influence;
and S600, finishing the dynamic modeling of the unmanned aerial vehicle under the rainfall weather condition on the basis of a small disturbance linear equation of the flexible unmanned aerial vehicle flight dynamic model.
2. The method of claim 1, wherein step S100 further comprises the steps of:
step S110, calculating the liquid water content in the air according to the rainfall rate;
step S120, according to the liquid water content in the airLWCEstablishing an air model as a continuous phase and a raindrop model as a discrete phase, performing fluid mechanics simulation on the aircraft by adopting a dynamic grid to perform unsteady forced oscillation motion, and calculating the impact force, the impact moment and the aerodynamic coefficient generated when raindrops impact the aircraft; and meanwhile, evaluating the dynamic pneumatic performance of the unmanned aerial vehicle, and calculating the pneumatic derivative of the unmanned aerial vehicle.
3. The method of claim 2, wherein the liquid water content of the air is determined by a model of the dynamics of the UAV based on rainfall weather conditionsLWCThe calculation formula of (a) is as follows:
Figure 863508DEST_PATH_IMAGE001
wherein the content of the first and second substances,ρ w is the rainwater density;Ris the rainfall rate;
Figure 513933DEST_PATH_IMAGE002
。
4. the method of claim 1, wherein the model of the rigid flight dynamics of the UAV taking into account rainfall effects is as follows:
Figure 31502DEST_PATH_IMAGE003
wherein the content of the first and second substances,
Figure 400166DEST_PATH_IMAGE004
is the coordinate of the mass center,
Figure 231856DEST_PATH_IMAGE005
is the angular velocity of the center of mass,
Figure 625535DEST_PATH_IMAGE006
is the speed of the mass center,
Figure 454950DEST_PATH_IMAGE007
as an external force, the pressure of the liquid is,
Figure 169966DEST_PATH_IMAGE008
the moment is the external moment,
Figure 805346DEST_PATH_IMAGE009
in order to be an external force caused by rainfall,
Figure 164783DEST_PATH_IMAGE010
in order to generate an external moment caused by rainfall,
Figure 289734DEST_PATH_IMAGE011
is a yaw angle, a pitch angle and a roll angle,
Figure 367412DEST_PATH_IMAGE012
is the moment of inertia of the aircraft about the coordinate axes,
Figure 134379DEST_PATH_IMAGE013
is the acceleration of gravity.
5. The method of claim 1, wherein the elastic motion equation is reduced by a modal truncation method based on modal coordinates, and the expression of the reduced elastic motion equation is as follows,
Figure 410640DEST_PATH_IMAGE014
wherein the content of the first and second substances,
Figure 847438DEST_PATH_IMAGE015
is a matrix of the quality of the system,
Figure 772930DEST_PATH_IMAGE016
is a matrix of the damping of the system,
Figure 953376DEST_PATH_IMAGE017
is a matrix of the stiffness of the system,
Figure 84143DEST_PATH_IMAGE018
、
Figure 816476DEST_PATH_IMAGE019
、
Figure 603166DEST_PATH_IMAGE020
respectively represents the displacement, the speed and the acceleration of the system,
Figure 446357DEST_PATH_IMAGE021
a generalized force matrix.
6. The method of claim 1, wherein the model of the flexible flight dynamics of the UAV under consideration of rainfall is as follows:
Figure 697210DEST_PATH_IMAGE022
wherein the content of the first and second substances,
Figure 475810DEST_PATH_IMAGE023
is the coordinate of the mass center,
Figure 874430DEST_PATH_IMAGE024
is the angular velocity of the center of mass,
Figure 396679DEST_PATH_IMAGE025
is the speed of mass centerThe degree of the magnetic field is measured,
Figure 502038DEST_PATH_IMAGE026
as an external force, the pressure of the liquid is,
Figure 74708DEST_PATH_IMAGE027
the moment is the external moment,
Figure 835991DEST_PATH_IMAGE028
in order to be an external force caused by rainfall,
Figure 20985DEST_PATH_IMAGE029
in order to generate an external moment caused by rainfall,
Figure 980850DEST_PATH_IMAGE030
is a yaw angle, a pitch angle and a roll angle,
Figure 101253DEST_PATH_IMAGE031
is the moment of inertia of the aircraft about the coordinate axes,
Figure 474466DEST_PATH_IMAGE032
is a matrix of the quality of the system,
Figure 338516DEST_PATH_IMAGE033
is a matrix of the damping of the system,
Figure 152889DEST_PATH_IMAGE034
is a matrix of the stiffness of the system,
Figure 834406DEST_PATH_IMAGE035
in the form of a generalized force matrix,
Figure 304701DEST_PATH_IMAGE018
、
Figure 598542DEST_PATH_IMAGE019
、
Figure 267420DEST_PATH_IMAGE020
respectively represents the displacement, the speed and the acceleration of the system,
Figure 995205DEST_PATH_IMAGE036
is the acceleration of gravity.
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