Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

53, 1, pp. 69-80, Warsaw 2015
DOI: 10.15632/jtam-pl.53.1.69

DYNAMICS OF AN UNGUIDED MISSILES LAUNCHER

Zbigniew Dziopa, Piotr Buda, Maciej Nyckowski, Rafał Pawlikowski
Kielce University of Technology, Faculty of Mechatronics and Machine Building, Kielce, Poland

e-mail: zdziopa@tu.kielce.pl

The paper discussed the modelling, examination of the dynamic properties and stability of
theWW-4 launcher of unguided short-rangemissiles NLPR-70. Remotely controlled arma-
mentmoduleZSMU-70, in thepresented configuration, is designed to combatground targets
in form of light armoured vehicles. The purpose of this paper is to present a physicalmodel,
a mathematical model and computer simulation of launcher motion during launching and
the first phase of flight of the missile. The virtual model is formulated in the vertical plane
and verified by experimental studies. The theoretical model corresponds to experimental
studies conducted at the military testing groundwith application of a high-speed camera.

Keywords: dynamics, launcher, unguided missiles, virtual model, experimental studies,
stabilization

1. Introduction

The paper presents theWW-4 launcher of short-range unguidedmissiles NLPR-70, as shown in
Fig. 1.

Fig. 1. TheWW-4 launcher of unguided missiles NLPR-70

The ZSMU-70 remotely controlled weapon consists of a launcher mounted on an armoured
motor vehicle (Dziopa, 2004, 2007). The launcher structure includes a platform with a guide
mounted on it. The guide can rotate relative to the platform performing the process of proper
angular setting selection. The unguided missile is located inside the guide. After the angular
settings are selected, the guide stops and the missile is launched. The rocket motor of the
missile, which generates thrust with known characteristics, is activated. A proper geometry of
the rocket motor nozzle leads to a force distribution which causes motion of the missile along
the launcher guide and at the same time its revolution round the longitudinal axis.
Thepresented system is designated to combat ground targets such as light armouredvehicles

and military infrastructure. The launch of the NLPR-70 missile from the WW-4 launcher was
recorded using a high-speed camera at themilitary testing ground.The vehicle does not perform
translatory motion while launching the missile. Firing is conducted from a stationary vehicle.



70 Z. Dziopa et al.

Figure 2 illustrates sample film frames which capture the first phase of the launcher motion.
The phase is characterized by direct contact between the moving missile and the guide.

Fig. 2. The first phase of the launcher motion

Fig. 3. The second and third phase of the launcher motion

The system is composed of two interacting objects: the launcher and the unguided rocket
missile. The motion of the launcher is induced exclusively by the missile launch. The missile
moves along the launcher guide, which results in a change of the characteristics of the system
inertia. The change involves the mass, weight distribution and the location of the system mass
centre (Biessonov, 1967). Figure 3 shows sample frames capturing the second and third phases
of the launcher motion. At the second phase, the missile leaves the guide and begins the flight
towards the target.The launcher stopsbeinga systemvariable in time.At themoment themissile
leaves the launcher, the system disintegrates into two objects: the launcher and the unguided
rocket missile. They are not yet independent objects as the external input starts affecting the
launcher. The input results from the influence of the rocket motor of the moving away missile.
The inputworks until the rocketmotor of themissile has no influence onmotion of the launcher.
It is only at the third phase that the launcher and unguided missile become two independent



Dynamics of an unguided missiles launcher 71

objects. Affected by the missile launch, the launcher vibration is excited. The missile performs
the trajectory resulting from the initial flight parameters developed on the launcher.
The motion of the armament module recorded under field conditions demonstrated the po-

ssibility of simplifying the spatial model down to two dimensions. The studied system is cha-
racterized by asymmetry of both geometry and the inertia characteristics. The verification of
the developed theoretical model has been conducted on the basis of the analysis of the pictu-
re recorded at the military testing ground. Therefore, the ZSMU-70 armament module can be
subjected to thorough analysis with computer simulation. It is significant from the perspective
of costs of the performed analyses, which are much higher in the case of studies at the testing
ground.Equally important is the aspect of testing the launcher via the computer under extreme
conditions which can be formulated by applying numerical methods.

2. Physical model of the launcher

The physical model, which is presented in Fig. 4 (Gantmacher, 1970; Osiecki, 1994; Swietlickij,
1963), has beendeveloped on thebasis of theWW-4 launcher of theNLPR-70unguidedmissiles.
Themodel presented in this figure illustrates the first phase of the launcher motion.

Fig. 4. Physical model of the missile launcher

The launcher, which is mounted on a motor vehicle, consists of two basic objects in form
of a platform and a guide.It ias assumed that the launcher along with the guide is positioned
on the vehicle symmetrically towards the vertical plane passing through the centre of mass of
the vehicle. The launcher is modelled in form of two masses and three deformable elements, as
in Fig. 4. The platform is a perfectly rigid body with mass mw and inertia moment Iw. The
platform is mounted on the vehicle bodywith two passive spring-damping elements with linear
parameters kw11 and cw11, and kw12 and cw12, respectively. The guide which is a perfectly rigid
body with mass mv and inertia moment Iv is mounted on the platform.
There is a rotational link between the guide and the platform. A deformable element with

linear parameters kw31 and cw31 respectively ias modelled at the place of attachment. Figure 4
presents also geometrical characteristics of the launcher, which is necessary for conductingan
analysis of the assembly dynamics.
The location of the solid body with mass mw and inertia moment Iw and the body of the

guide with mass mv and inertia moment Iv at any point in time are determined in Cartesian
dextrose rectangular coordinates system. The following coordinates are the reference system:

a) coordinates definingmotion of the platform: 0wxwywzw, Swxwywzw, Swξwηwζw,

b) coordinates definingmption of the guide: 0vxvyvzv, Svxvyvzv, Svξpηpζp,



72 Z. Dziopa et al.

The number of degrees of freedom resulting from the formulated structure of the launcher
model describing the disorders of the primarymotion in the vertical plane equals 3. Two inde-
pendent generalized coordinates are adopted in order to determine the position of the platform
with mass mw and inertia moment Iw at any moment in time: yw – vertical relocation of the
centre of mass Sw of the platform, ϑw – revolution angle of the platform round the axis Swzw.
One independent generalized coordinate has been adopted to determine the positions of the

guide with mass mv and inertia moment Iv at any moment in time: ϑv – rotation angle of the
guide round the axis Svzv.
In the general case, the missile is an object with variable mass and weight distribution

(Biessonov, 1967). Missile parameters such as mass mp and the tensor of moment of inertia Îp
are functions variable in time in the general case. Thepositions of the solid body at anymoment
in time are indicated by Cartesian orthogonal dextrose systems of rectangular coordinates. The
following systems of coordinates constitute the systems of reference.
The systems of coordinates definingmotion of the missile at the launch from the guide:

a) the system of coordinates defining the lifting motion of the missile:

– 0xyz, 0vxvyvzv, Svxvyvzv and Svξpηpζp are systems of coordinates which have been
discussed earlier, define one motion of the guide. The guide imposes constraints on
themissile motion. Themissile performs complexmotion consisting of liftingmotion
performed by the guide and motion of the missile relative to the guide. In the case
of launching the missile from the guide the system of coordinates 0xyz, 0vxvyvzv,
Svxvyvzv and Svξpηpζp define also the lifting motion of the missile;

b) the systems of coordinates defining the relative motion of the missile:

– Spξpηpζp is a system of coordinates performing linearmotion relative to the system of
coordinatesSvξvηvζv.Thebeginningof the systemof coordinatesSp at anymoment in
time coincides with the centre ofmass. The condition of parallelism is always fulfilled
for theaxesSpξp‖Svξp,Spηp‖Svηp andSpζp‖Svζp, correspondingone toanother.Under
the influence of the rocket booster, themissile centre of mass Sp shifts along the axis
Svξp;

– Spxpypzp is a system of coordinates performing rotarymotion relative to coordinates
Spξpηpζp. The axes Spxp,Spyp andSpzp are rigidly linked to the bodyof themissile in
suchaway that theybecome itsmain central inertia axes.Thecondition of parallelism
is always fulfilled for the two axes Spξp‖Spxp. Under the influence of the booster, the
body of the missile turns around axis c in accordance with the change of the tilting
angle ϕp.

The number of degrees of freedom resulting from the formulated structure for the model of
the kinematic pair: guide-missile which describes motion of the missile relative to the guide in
the vertical plane equals 2.
Two independent generalized coordinates are adopted in order to determine the position of

the missile with mass mp and inertia moments Ipxp, Ipzp at any moment in time: ξp – linear
relocation of the centre of mass Sp of the missile along the axis Svξp, ϕp – rotation angle of the
missile round the axis Spξp.

3. Mathematical model of the launcher

Themathematical model of the launcher in the vertical plane was developed on the basis of the
adopted physical model (Gacek and Maryniak, 1987; Swietlickij, 1963). The discussed system
was brought to the form of a structural model of discrete structure, therefore it is described



Dynamics of an unguided missiles launcher 73

by differential equations with ordinary derivatives represented by five independent generalized
coordinates (De Silva, 2007; Gantmacher, 1970).
Five independent coordinates were adopted to determine themotion of the launchermodel:
• platform – perfectly rigid body: yw, ϑw
• guide – perfectly rigid body: ϑv
• missile – system variable in time: ξp, ϕp.
These are the equations of motion

(mw+mv+mp)ÿw− (mv+mp)hvϑ̈w sinϑw+mpξpϑ̈v cosϑv
−(mv+mp)hvϑ̇2w cosϑw−mpξpϑ̇2v sinϑv+mpξ̇pϑ̇v cosϑv+kw11λw11
+kw12λw12 − cw11λ̇w11 − cw12λ̇w12 =−(mw+mv+mp)g

[Iw+ Ipzp + Iv+(mv+mp)h
2
v]ϑ̈w+[Ipzp +mphvξp(cosϑw sinϑv− sinϑw cosϑv)]ϑ̈v

−(mv+mp)hvÿw sinϑw−mphvξ̈p(cosϑw cosϑv+sinϑw sinϑv)
+2mphvξ̇pϑ̇w sinϑw cosϑv−2mphvξ̇pϑ̇v sinϑw cosϑv
+mphvξpϑ̇

2
v(cosϑw cosϑv− sinϑw sinϑv)+kw11lw1λw11 −kw12lw2λw12

−kw31λw31 − cw11lw1λ̇w11 + cw12lw2λ̇w12 + cw31λ̈w31
=(mv+mp)ghv sin(ϑw+ϑwst)

(Iv+ Ipzp +mpξ
2
p)ϑ̈v+mpξpÿw cosϑv

+[Iv+ Ipzp +mphvξp(cosϑw sinϑv− sinϑw cosϑv)]ϑ̈w+2mpξpξ̇pϑ̇v
+mphvξpϑ̇

2
w(sinϑw sinϑv+cosϑw cosϑv)+kw31λw31 − cw31λ̇w31

=−mpgξp cos(ϑv +ϑvst)
mpξ̈p−mphvϑ̈p(cosϑw cosϑv+sinϑw sinϑv)+mpÿw sinϑw
+mphvϑ̇

2
w(sinϑw cosϑv− cosϑw sinϑv)+mpξpϑ̇2v =−mpgsin(ϑv+ϑvst)+Pp

Ipxpϕ̈p = Mp

where

λw11 = yw+ywst+ lw1(ϑw+ϑwst)−yw11 λ̇w11 = yw+ lw1ϑ̇w−yw11
λw12 = yw+ywst− lw2(ϑw+ϑwst)−yw12 λ̇w12 = ẏw− lw2ϑ̇w− ẏw12
λw31 = ϑv+ϑvst−ϑw+ϑwst λ̇w31 = ϑ̇v− ϑ̇w

and Pp – thrust of the rocket motor, Mp –moment of force, generated by the rocket motor.
Three static displacements appear in the equations ofmotion for the launcher in the vertical

plane:
• platform: ywst, ϑwst
• guide: ϑvst.

These are the static equilibrium equations

kw11(ywst+ lw1ϑwst)+kw12(ywst− lw2ϑwst)+(mw+mv+mp)g =0
kw11lw1(ywst+ lw1ϑwst)−kw12lw2(ywst− lw2ϑwst)−kw13(ϑvst+ϑwst)
−(mv+mp)ghv sinϑwst =0

kw13(ϑvst+ϑwst)= 0

Themathematicalmodel can be classified as a coupled systemwith time-varying coefficients,
determined, variable in time, dissipative and bounded, with five degrees of freedom.Thismodel
corresponds to experimental studies.



74 Z. Dziopa et al.

4. Vibro-isolation system for controlling vibrations of the launcher

The purpose of this paper is to present the vibro-isolation system reducing the occurring vi-
brations. Twomethods for eliminating vibrations have been applied in the process of computer
simulation (Engel and Kowal, 1995; Inman, 2006). Passive vibro-isolation is the first method,
while the second is the hybrid stabilizationmethod (Dziopa, 2003, 2008). The rheological Voigt-
Kelvinmodel,whichhasbeenparametricallymodified, is used in thepassivemethod.Thehybrid
method uses control devices engaged in series in the weightless system with restitutional and
dissipative properties. The applied control systems operate independently of each other. Each of
them stabilizes only one point of attachment of the passive system. The adjustment takes place
in a closed system(Inman, 2006).Apassive element in the formof theVoight-Kelvinmodel along
with the controlled executive system as an electro-hydraulic servo, two acceleration sensors and
a numerical processor make the control loop. Using a double integrator, the measuring system
transmits the realized signal and the forcing signal to the numerical processor, which on their
basis indicates the control signal. The formulation of the signal through the numerical processor
runs in accordance with the adopted control algorithm. The applied control systems provide
both linear and angular stabilization of the launcher (Dziopa, 2003, 2008). The diagram of the
control system for the US11 device is presented in Fig. 5.

Fig. 5. Control system diagram for the US11 device

The adopted control algorithm realized in the process of simulation for the US11 device has
the following form

uw11 = ks11yw11 +ks21yw21 u̇w11 = ks11ẏw11 +ks21ẏw21

For the device US12

uw12 = ks12yw12 +ks22yw22 u̇w12 = ks12ẏw12 +ks22ẏw22

where: yw11, yw12 – signals from the carrier, yw21, yw22 – signals from the platform, ks11, ks12,
ks21, ks22 – control coefficients.

5. Flight model missile

The rocketmissiles play an important part in the operation of the armamentmodule ZSMU-70.
Whether the object of attack will be neutralized depends directly on themissile. Effective firing
of the unguided short-range rocketmissile requires providing itwith proper comfort. Themissile



Dynamics of an unguided missiles launcher 75

may be excited to vibrate directly by the launcher which imposes constraints on the location
and velocity of their points. In that case launcher vibrations may lead to failure in hitting the
target with the missile already before it is launched (Dziopa, 2004). The launcher is one of the
objects of thewhole assembly and the disturbance it generates result from the interaction, which
is the consequence of feedback within the system. Themovement of the missile on the launcher
is conditioned by the structure guide-missile. The rocket motor, whose function is to impart
proper linear and angular velocity to the missile, is located at the rear end of the missile body.
Therefore, on the launcher, themissile moves along the guide and rotates simultaneously round
its own longitudinal axis (Gacek and Maryniak, 1987). After launching, the missile continues
its movement towards the target. Although the launcher has no direct possibility to affect the
missile during its flight, the interference in this phase of the flight takes place at the moment
the missile leaves the guide. In one moment of time the system disintegrates in a natural way,
i.e. it is divided into two independent systems in the form of the launcher and missile. At
this moment, the initial kinematic parameters of the rocket flight are determined(Dziopa, 2006;
Dziopa et al., 2010). The flight path is shaped, inter alia, by the value of these parameters. The
launcher motion may cause the rocket to follow an adverse trajectory and consequently to miss
the target.The missile moves in the gravitational field and in the Earth atmosphere (Żyluk and
Pietraszek, 2014; Żyluk, 2014). The adopted model of forces affecting the rocket is presented in
Fig. 6.

Fig. 6. The model of forces affecting the missile during its flight

Due to comlexity of themathematical model of the rocketmissile, only the dependencies re-
presenting the equations ofmotion are presented in the general form.The individual parameters
appearing in the equations of motion are either described by functions or constitute empirical
dependencies which are approximated in the process of numerical simulation.
The equations of missile motion in space are following (Dziopa, 2006; Dziopa et al., 2010;

Sibilski, 2004):
— equations of the progressive part of motion in the system of coordinates connected to the
flow Spxvyvzv

mpVp = Ps[sinψp sinχp+cosψpcosχpcos(θp−γp)]−Pg cosχp sinγp
+Pax[sinψp sinχp+cosψpcosχpcos(θp−γp)]
+Pay{sinϕp[sinψpcosχpcos(θp−γp)− cosψp sinχp]− cosϕp cosχp sin(θp−γp)}
+Paz{sinϕp[sinψpcosχpcos(θp−γp)− cosψp sinχp]− cosϕpcosχp sin(θp−γp)}

mpVpγ̇pcosχp =Ps cosψp sin(θp−γp)+Pg cosχp+Paxcosψp sin(θp−γp)
+Pay[sinϕp sinψp sin(θp−γp)− cosϕp sin(θp−γp)]
+Paz[sinϕp sinψp sin(θp−γp)− cosϕp sin(θp−γp)]



76 Z. Dziopa et al.

mpV̇pγ̇pcosχp = Ps[cosψpcosχpcos(θp−γp)− sinψpcosχp]−Pg sinχp sinγp
+Pax[cosψp sinχpcos(θp−γp)− sinψpcosχp]
+Pay{sinϕp[sinψpcosχpcos(θp−γp)+cosψp sinχp]− cosϕp sinχp sin(θp−γp)}
+Paz{sinϕp[sinψp sinχpcos(θp−γp)+cosψpcosχp]− sinϕp sinχp sin(θp−γp)}

— equations of the spherical part of motion in the system of coordinates Spxpypzp related to
the rocket

Ipxω̇px+(Ipz −Ipy)ωpyωpz = Max Ipyω̇py+(Ipx− Ipz)ωpxωpz = May
Ipzω̇pz +(Ipy− Ipx)ωpxωpy = Maz

where: Vp – velocity of the rocket mass centre, γp,χp – inclination angle of the vector of de-
viation of the missile velocity, θp,ψp,ϕp – inclination angle, deviation, tilt of the rocket body,
ωpx,ωpy,ωpz – components of the vector ofmissile angular velocity, mp – rocketmass, Ipx,Ipy,Ipz
– principal central moments of inertia, Pax,Pay,Paz – aerodynamic force vector components,
Max,May,Maz – vector components of the aerodynamicmoment, Pg – force of gravity, Ps – roc-
ket motor thrust.

6. Numerical simulation

The formulatedmodel of themissile launcher allowed us to conduct numerical simulation aiming
to analyze the launcher motion while launching the missile and during its flight (Dziopa, 2004,
2006; Dziopa et al., 2010). The present configuration of the launcher is dependent on angular
settings resulting from the location of the target. During the launch of themissile, the launcher
is a systemvariable in time (Biessonov, 1967). Itsmass as well as its weight distribution change.
Sample results of the conducted numerical simulation are presented below.
Figure 7 presents variability courses of the angle of inclination of the launcher guide.

Fig. 7. Variability course of the launcher guide inclination angle

Figures 8 present variability courses of the displacementin of the launcher platform in the
vertical motion.
Figure 9 shows the variability course of the inclination angle of the guide in the case of active

and passive mounting of the platform. Within the whole range of variability of functions, the
hybrid vibro-isloation system leads to a significant reduction of angular vibrations of the guide.
The application of the passive system only does not provide sufficient vibro-isolation.
Figure 10 illustrates a comparisonof the lineardislocation of theplatform in the case of active

and passive mounting. Within the entire scope of the function variability, the hybrid system of
vibro-isolation entails definite reduction of linear vibrations of the platform. The application of
the passive system exclusively does not provide sufficient vibro-isolation.



Dynamics of an unguided missiles launcher 77

Fig. 8. The course of variability of launcher platform dislocation

Fig. 9. Comparison of the variability course of the inclination angle of the platform in the case of its
active and passive mounting

Fig. 10. Comparison of the linear dislocation of the platform in the case of its active and
passivemounting

Sample results of thenumerical simulation of flight of theunguided short-range rocketmissile
arepresentedbelow.After launching, the rocket starts its flighthavingvarious initial parameters.
Thequantitative andqualitativediversificationof the initial parameters results fromthedynamic
reaction appearing in the launcher system from which the missile is fired. One of the initial
parameters is the inclination angle of the rocket θp determined at the moment of launching.
The results include three values of the initial inclination angle of the rocket: 1 – θp = 10deg,
2 – θp =8deg, 3 – θp =6deg.
A slight change in the inclination angle of the rocketmissile at themomentwhen themissile

leaves the launcher guide significantly changes the flight trajectory, as in Fig. 11. Missiles 2
and 3 realize a wrong trajectory and, as a result, miss the target. The courses of variability of
the angular velocity in the tilt motion of missiles 1, 2, and 3 are the same, see Fig. 11.
It results from the conducted research that it is the angular velocity in the inclination

movement θ̇p that has the most significant influence on the performance of the rocket during
its flight. It is the angular velocity defined at themoment themissile leaves the launcher guide.
The flight path of the rocket depends not only on the value of this kinematic quantity, but also



78 Z. Dziopa et al.

Fig. 11. Flight trajectory and angular velocity in the tilt motion of the rocketmissile

on its direction. The results include three values of the initial angular velocity of the rocket in
the inclination movement: 1 – θ̇p =0rad/s, 4 – θ̇p =−0.2rad/s, 5 – θ̇p =−0.4rad/s.
An insignificant change in the angular velocity of the rocket missile θ̇p at the moment when

the missile leaves the launcher guide considerable changes the flight trajectory, see Fig. 12.
Missiles 4 and 5 realize a wrong trajectory and consequentlymiss the target. Variability courses
of the angular velocity in the tiltmotion of rocketmissiles 1, 4, and 5 are the same as in Fig. 12.

Fig. 12. Flight trajectory and angular velocity in the tilt motion of the rocketmissile

7. Conclusions

An analysis of launching and flight of the unguided rocket missile NLPR-70 from the launcher
WW-4 of the remotely controlled armament module ZSMU-70 has veen conducted as a part of
the work. The launcher is positioned on amotor vehicle which is in the static equilibrium state
at the moment the rocket motor is activated. The process of launching the missile from this
armament module has been recorded with a high-speed camera at the military testing ground.
The analysis of the recorded motion picture allowed us to evaluate the kinematic quantities
characteristic for the launcher andmissile performance.
A theoretical model of the launcher andmissile motion has been developed after conducting

the experimental studies and interpreting the results. The equations of the systemmotion repre-
senting themathematical model have been derived on the basis of the physical model which has
been formulated. The recordedmotion of the armamentmodule under field conditions indicated
the possibility to design a virtual model with two dimensions. The theoretical model presented
in the paper has been verified in experimental studies. Computer simulation and an analysis of
the physical phenomena has been conducted taking into consideration analytical dependencies
relating to the launcher motion and the unguidedmissile while launching.The inputs generated
in the system while launching the missile have been determined as well as how they affect the
launcher and the extent of the initial flight parameters. From the perspective of hitting the
target of a certain surface, it is important for the initial missile flight parameters to allow that
happen.The conducted considerations lead to the conclusion that the initial setting of the guide



Dynamics of an unguided missiles launcher 79

may differ explicitly from their values at themoment of launching themissile. For the unguided
missiles it is specifically unfavourable as they cannot change their trajectorywhile flying.Hitting
the target of a certain surface with the missile launched from the assembly under investigation
is very problematic. The designed model allows for a comprehensive analysis of the launcher
dynamics when launching the uncontrolledmissile. It also enables evaluation of the initial flight
parameters of the missile from the perspective of target reachability.
The paper presents a comparison of variability courses of selected physical quantities charac-

terizing responses of the launcher to themissile launch in the case of active andpassivemounting
of the launcher platform. This allows us to evaluate the effectiveness of the implemented laun-
cher stabilization system in form of two control systems operating independently of each other.
The characteristic feature of the developed system is stabilization of each control systemby only
one point of attachment of the platform. The application of the system reducing vibrations of
the platform determines the change of responses of the individual objects of the assembly to the
occurring input. The vibrations of the launcher caused by themissile launch are reduced by the
system stabilizing the platform.The passivemounting of the platform conveys disturbances and
excites both the linear and angular vibrations of the launcher. The change of the passivemoun-
ting into active one significantly decreases the level of vibrations of the guide. It is important
in the case of input occurring from the side where the gases are emitted by the rocket motor
of the missile moving away from the launcher. Due to application of the active mounting, the
input will not excite the guide to intensive vibrations. In the case of launching another missile,
the reduced vibrations of the guidewill not affect its launch in a negative way. Themovement of
the guide provides “comfort” for the missiles which are launched, and simultaneously improve
the effectiveness in reaching the target. The stabilization system does not entirely eliminate the
unfavourable phenomenon of rapid increase in the values of linear and angular acceleration of
the platform themoment the missile leaves the guide, but reduces it.
It results from the research that the initial parameters of unguided missile flight affect its

trajectory. The range of initial parameters of flight is determined by the dynamic characteristics
of the launcher. The angle of setting the guide at themoment of launching themissile, but also
its angular velocity in the inclination movement are extremely important. Both the value and
the direction of the vector of the angular velocity are significant. Particularly adverse is the
angular velocity resulting from the inclination of the rocket towards the Earth. The system of
active stabilization of the launcher should be introduced in order to increase the effectiveness
of the unguided rocket missile. The current structure of the remotely controlled module of the
armamentZSMU-70 does not guarantee high effectiveness in the case of firing at a ground target
whose overall dimensions are inconsiderable.

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Manuscript received December 5, 2013; accepted for print July 21, 2014