Development and twisting of space cable system relative to centre of gravity with help of gravity and internal forces

FIELD: transport.

SUBSTANCE: invention relates to space cable systems (SCS) and can be used for the transfer of SCS to a spinning mode in the orbit plane without the application of jet engines. SCS development is executed from its initial compact state in the circular orbit by the repulsion of objects at a low relative speed. SCS end weights are connected by a cable, its length being varied by a cable feed-haul-in device arranged on one of the end objects. The objects are separated by a vector of local peripheral speed, for example, by a pusher. The objects are driven by a start pulse to separate the objects in practically free paths at the free feed of the cable. The cable development is terminated by the SCS transfer to a stable mode of associated pendulum motion at the stretched preset-length cable. At a definite range of angular phases of this mode the SCS objects are stretched by hauling in the cable at a definite constant speed. This results in changing the SCS into the spinning mode at a preset power integral and fixed final end of the cable.

EFFECT: relaxed weight-size constrictions of SCS, enhanced performances.

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The invention relates to space technology, mainly to tethered space systems (KTS). The invention can be used to translate the CCC in the mode of its rotation about the center of mass (space "slingshot") in the plane of the orbit without the use of jet propulsion and, accordingly, without the cost of a working body on this maneuver.

Under space tether system understand the totality of the two SPACECRAFT (SC) connected by a long thin rope. Potential areas of practical use of the CCC suggest three sustainable mode of motion CCC [1]: steady-state mode (mode gravitaional), the libration mode of oscillation and rotation mode. The General condition for the realization of sustainable modes of motion of the CCC is the motion of its center of mass in a circular orbit with a taut rope of fixed length.

In rotation mode under the action of gravitational and centrifugal forces on the AC ligament occurs shallow artificial gravity. This effect can be used to create comfortable conditions for life and work of the astronauts, for cultivation in the space of plants, to refuel spacecraft fuel from a remote terminal, for conducting medical, biological, technological, and other experiments in low gravity, the level of which the reg is activated [1-3].

Rotating the CCC can also be used to generate a conductive wire of an alternating electric current, for monitoring of physical fields, to perform various orbital maneuvering space objects without the cost of fuel. Changing in a certain way the cable length of the CCC, it is possible to carry out the evolution of the parameters of its orbit, as well as mutual maneuvering limit objects ligaments. When the SC separation from the rapidly rotating ligament (space "slingshot") you can tell SPACECRAFT large enough extra speed to translate it to a higher or lower orbit, reentry or transfer to the trajectory of interplanetary flight. Using built in a certain way in space collectively, the "sling shot", you can establish a permanent transport channel in space [6-8].

Sustainable modes of motion CCC listed above are integral energy and quantitatively can be ranked dimensionless energy angular motion of a stretched ligament relative to its center of mass. By definition centuries Beletsky [1], the energy integral is dimensionless quantity whose value is determined by the initial conditions for the angular motion:

$$h={\stackrel{}{\stackrel{}{\phi }}}^{2}mo>\; -3{\cos }^2\phi ={\stackrel{}{\stackrel{}{\phi }}}_o^2-3{\cos }^2{\phi }_o$$,

where φ is the phase of the angular position of the line of sight objects CCC;

$$\stackrel{}{\stackrel{}{\phi }}=\stackrel{}{\phi }/{\omega }_c$$- the speed of angular movement of the CCC;

$${\omega }_c=\sqrt{\mu /r_c^3}$$- the angular velocity of the orbital motion of the center of mass CCC;

r_with- geocentric radius of the circular orbit of the center of mass of the CCC (Fig.1);

µ - constant gravitational field of the Earth.

Mode gravitaional CCC the energy integral h_g=-3.

Mode librational oscillations with amplitude φ_o∈(0°, 66°) the value of the integral energy varies in the range h_Lieb=(-3; -0,5).

Mode associated rotation value of the energy integral h_BP>0.

The translation of the CCC in the steady driving mode with the specified value of the integral energy on the cable of a given length is carried out, the initial state is, when two SPACECRAFT as a whole, make the movement of the original circular orbit so that the cable is compactly stacked on the feeder-sampling, located on one of the AC.

In the technical aspect of the task of translating the CCC in the steady driving mode is not trivial, since it involves the simultaneous solution of two main tasks:

1) deployment of the cable to a predetermined length and

2) providing the required values of the parameters of the position and velocity at the end of the area of deployment of the CCC.

The deployment of the cable to a predetermined length can be technically implemented in many different ways:

- using a pulsed allowed - passive deployment;

- using a pulsed allowed and further control the power cable tension - active deployment;

using continuous thrust jet engines, installed on one or two AC cords - active deployment;

using management integration of reactive forces and elastic forces of the tension of the rope.

In the first two embodiments, the deployment is due to internal forces of the system.

Required terminal conditions at the end of the plot cultivation can be implemented:

- selection of the initial conditions of motion in repulsion and passive deployment CCC;

- selection of initial conditions the motion and the parameters of force control cable tension during deployment CCC;

by the power of the sample buffer and changes the moment of inertia angular motion;

using jet engines.

In the first three embodiments, the transfer of technology for sustainable mode of motion is due to internal forces of the system.

Various combinations of management options to deploy the rope and options to achieve the desired terminal conditions define the various ways of transfer of technology for sustainable modes of motion.

Consider the well-known and investigated methods of deploying and twist space tether systems.

In [4, 6] is described and investigated using mathematical models method of deploying a cable and transfer the CCC mode librational oscillations [6] and the rotation mode [4] with a jet engine mounted on one of the AC ligaments. The process of twisting the CCC is performed in three stages:

1. First start up of the engine for cultivation of objects to a certain milestone and pre-twist of the CCC.

2. Passive breeding KA using centrifugal forces on a given length of cable. The relative velocity at the end of the plot cultivation is equal to zero.

3. The second burn of the engine at a fixed length of cable to achieve the specified parameters of the rotation.

The conditions that minimize the consumption of the working fluid to perform the maneuver.

In [5] is described and IP is ladawan way "gravitational spin two SPACECRAFT using two jet engines, installed on the SPACECRAFT. The process of twisting the CCC is performed in three stages:

1. Starting the engines for cultivation KA and unwinding of the cable to a length exceeding the desired value. At the end of the first stage of the CCC will be switched to the librational motion of the position of the maximum amplitude.

2. Passive libratory motion of the CCC to the output of the angular position of the line of sight its leaf objects in the neighborhood of the local vertical.

3. Rapid contraction of the CCC in the vicinity of the local vertical by the power of the sample of the cable to reduce the moment of inertia and translation of the CCC in the rotation mode.

Investigated three laws sampling of the rope: a contraction with constant speed, the sampling of the rope at a constant power winch and contraction at a speed proportional to the distance between the SPACECRAFT. The described method is preferred according to the criterion of flow of the working fluid.

The advantage of these methods is the possibility of implementing any energy modes rotation CCC arbitrary length. The disadvantages of these methods include:

- the complexity of the design due to the presence of jet engines and reserves of the working fluid to them and, consequently, low reliability;

- the finite and the finite energy resource;

program motion control in both methods require the nalitch the e non-trivial control system.

Devoid of these shortcomings, the group ways of twist, which is based on the sequential ejection spring plunger from the Board of massive orbital platforms leaf CCC [2]. The methods differ in the initial conditions of firing and conditions of supply cable when deploying the CCC. The ways have a common characteristic:

1. Before deploying SPACECRAFT docked at the orbital platform, which moves in an orbit, almost coincident with the desired orbit the center of mass of the CCC. The cable is compactly stacked on the device for depositing and filing, located on one of the AC ligaments.

2. The axis of the spring plungers are oriented in the plane of the original orbit. Department of the pulse due to internal forces of the system. The magnitude of the speed pulse separation unit meters per second.

3. The mass of the SPACECRAFT, forming a pair, are 1-10 kg, cable length is 100 meters, the angular velocity of the rotation system is 0.1-1.0^-1the deployment time and the spin system is a few percent from the orbital period orbital platform. The advantage of these methods is the simplicity of technical and technological implementation twist the CCC in the plane of the orbit, as well as the possibility of multiple launch aboard an orbital platform rotating the CCC without flow of the working fluid to conduct the maneuver.

the main drawback of these methods is significant mass-dimensional constraints imposed on the CCC.

The proposed method of deployment and twist the CCC about the center of mass by gravity and internal forces accumulates merits considered analogues and practically free from the above disadvantages. The method has no restrictions either on the weight of the AC ligament, nor on the length of the connecting cable or consumption.

The closest analogue among the considered methods of twist of the CCC is the way "gravitational spin two SPACECRAFT using two jet engines [5], which is considered as a prototype. The main difference of the proposed method of spin from the prototype is the use of the internal forces of the system at the first stage of the maneuver, which allows to exclude the use of jet engines. The deployment of the CCC in this case, the orbital plane of its center of mass is from the initial monolithic state system allowed by objects with small initial relative velocity. Leaf mass CCC m_i, i=1, 2 are connected by a thin rope, the length of which may vary with the feeder-fetch the rope. Feeder-sampling can be installed on one of the AC ligaments. In the initial position before the separation system performs a monolithic movement in a circular orbit of radius r with. The separation of objects is made by the line vector of the local circular speed mechanical pusher. The potential energy of the pusher provides a starting pulse separation ΔV. Related rope objects are removed from each other for free trajectories under free supply cable. The process of deployment of the cable ends with a translation of the CCC in the phase state, from which it passes into a sustainable mode of the associated pendulum motion on the taut rope of fixed length.

Graphically scheme of maneuver twist CCC presented on figure 2 in the form of the locus of the vectors of the limit of the masses [9]. To equal the limit of the masses ligament their trajectory of the relative motion is almost symmetric about the center of mass. Technologically maneuver twist the CCC can be divided into several stages:

Stage 1. The point O in Fig.2, 3 - pulse transversal separation of the objects of the CCC on the original orbit About_withand the transition SPACECRAFT into an elliptical orbit O₁and O₂.

Stage 2. The trajectory 0-1 in Fig.2. Passive deployment of the CCC when the free supply of rope.

Stage 3. The trajectory 1₂-2. Associated pendulum movement of the CCC on the taut rope of fixed length.

Stage 4. The trajectory 2-3. The contraction of the CCC by the power of the sample of the rope at a constant speed.

Stage 5. Plot tract the series 3-4. The CCC rotation with a given value of the integral energy for a fixed length of rope.

The proposed method of deployment and twist the CCC with respect to its center of mass is studied on a mathematical model with the following assumptions:

movement of the CCC is considered in the Newtonian field of attraction;

- rope is lightweight, flexible and inextensible thread of high modulus material;

- passive deployment CCC (section 0-1) supply cable from the device occurs without resistance;

- contraction of the CCC is made with a constant sampling rate of rope.

The research was conducted under the following problem statement. In the initial state of the CCC, consisting of two SPACECRAFT with a mass m_ii=1, 2, monolithic block moves in a circular orbit with the geocentric radius r_with. The connecting cable is laid on the feeder-sampling, which is installed on one of the AC. The device allows you to implement a free supply cable when removing the AC relative to each other after they are allowed, and to produce power sample of the rope at a constant speed winder, a=const. The repulsion KA is along the line of the orbital velocity vector using a spring plunger that implements the starting pulse speed separation ΔV. The maximum value of the velocity of the winder rope and pulse rate rastali the project for the AC are of the same order and do not exceed 10 m/s

It is necessary to determine the magnitude of the pulse is allowed, the trajectory parameters passive deployment, pendulum motion and force fetch cable at speeds that allow to CCC from the initial state in the rotation mode with a given value of the energy integral h_BP>0 for a given length of rope.

The solution with the purpose of generalization of its results are presented in dimensionless parameters and variables:

-$$\stackrel{}{m}=m_2/m_1$$- mass ratio leaf CCC;

-$$\Delta \stackrel{}{V}=\Delta V/V_C$$- the dimensionless momentum allowed, where$$V_C=\sqrt{\mu /r_C}$$- the circular velocity of the center of mass CCC;

-$$\stackrel{}{l}=l/r_C$$- the relative length of rope.

stage 1. For definiteness, assume that when the repulsion SPACECRAFT with a mass m₁got an accelerating pulse velocity ΔV₁and KA Museum ₂- brake pulse ΔV₂. On the basis of additivity of momentum (quantity of motion) - "the momentum of the system is equal to the sum of the momenta of its individual particles, regardless of the possibility of neglecting the interaction between them" [10] taking into account the limitations on the capacity of the pusher ΔV₁+ΔV₂=ΔV, get the pulse rate allowed:

$$\Delta {\stackrel{}{V}}_1=\frac{\stackrel{}{m}}{\stackrel{}{m}+1}\Delta \stackrel{}{V},\Delta {\stackrel{}{V}}_2=\frac{1}{\stackrel{}{m}+1}\Delta \stackrel{}{V}.\text{(2)}$$

Calculation of motion in elliptic orbits O₁and O₂(Fig.3), the geometric parameters of which depend on the pulse speed allowed:

$${\stackrel{}{p}}_1=\frac{p_1}{r_C}={(1+\frac{\stackrel{}{m}}{\stackrel{}{m}+1}\cdot \Delta \stackrel{/mo>}{V})}^2,{\text{e}}_{\text{1}}={\stackrel{}{p}}_1-1;$$

$${\stackrel{}{p}}_2=\frac{p_2}{r_C}={(1-\frac{1}{\stackrel{}{m}+1}\cdot \Delta \stackrel{}{V})}^2,{\text{e}}_{\text{2}}=1-{\stackrel{}{p}}_2.$$

Relative and absolute limit movement of the masses along these trajectories are discussed in detail in the monograph [9]. It is established that these trajectories, there are two singular points, in which the speed of the relative movement of the leaf mass is zero and acceleration have opposite signs. These special points are the boundaries of the reverse relative motion of the SPACECRAFT. The angular position of the singular points does not depend on the mass ratio objects of the CCC and the magnitude of the impulse speed allowed range of values ΔV<30 m/C. These points are located on elliptical orbits (Fig.4) almost simme the ranks relative to the point Of separation of the CCC on the starting orbit.

The angular position of the first singular point: ε₁₁=42,5⁰(true anomaly ϑ₁₁=to 317.5°) and ε₁₂=41° (ϑ₁₂=139°). The arrival time of the end bodies in this point, expressed in units of the orbital period of the orbit of the center of mass, equal to$${\stackrel{}{t}}_{pe\mathrm{in}}$$=0,886. The distance between the end bodies$${\stackrel{}{l}}_{pe\mathrm{in}}=19,32\cdot \Delta \stackrel{}{V}$$. In the first special point begins the reverse motion mode of the CCC and the associated need a sample free of the rope. This process is completed in the second special point, and the parameters of relative motion of the CCC meet the conditions bumpless transfer CCC mode associated vibrational motion. In Fig.2 the second special point indicated by the symbols "l₁and l₂". The angular position of the second singular point:

ε21=ϑ₂₁=40,5° and ε₂₂=41° (ϑ₂₂=221°). Time of arrival at the point of$${\stackrel{}{t}}_1\approx 1,113$$. The distance between the end bodies$${\stackrel{}{l}}_1=18,4\cdot \Delta \stackrel{}{V}$$. If we fix the length, the system will switch to the associated pendulum motion with the initial conditions:

,

and the value of the integral energy:

$$h_1={\stackrel{}{\stackrel{}{\phi }}}_1^2-3{\cos }^2{\phi }_1=0,003.\text{(5)}$$

This value of the energy integral is close to zero and corresponds to the transition state between librational and rotational movements of the CCC.

stage 2. Associated pendulum movement of the CCC on the taut rope is described by equations [9]:

$$\stackrel{}{\stackrel{}{\phi }}+2a/\stackrel{}{l}(\stackrel{}{\stackrel{}{\phi }}+1)+3\sin \phi \cos \phi =0,$$

$$n_C={\stackrel{}{\stackrel{}{\phi }}+1)}^2-1+3{\cos }^2\phi ,$$

where n_withlocal overload of the power cable tension$$F_n=m_1{m}_2/(m_1+m_2)\cdot l\cdot {\omega }_c^2\cdot n_c$$.

If we fix the cable length, the angular movement of the CCC on the interval φ∈(φ₁that & Phi;₂) can be described by the equation$$\stackrel{}{\stackrel{}{\phi }}+3\sin \phi \cdot \cos \phi =0$$.

The movement of the CCC at this stage is determined by the angular phase of initial and final States [9]:

$${\stackrel{}{t}}_{12}=\frac{1}{2\pi \sqrt{3}}\cdot \ln \left(\frac{1+\sin {\phi }_1}{1+\sin {\phi }_2}\cdot \frac{\cos {\phi }_2}{\cos {\phi }_1}\right)$$.

Stage 3. The contraction of the CCC at a constant speed. The final state of the system after tightening to the specified level of energy of rotation h_BPis uniquely determined by the phase angle φ₃residual length of the rope l₃and increment the dimensionless energy of rotation of Δh. According to [1], the parameters of the final status of the CCC are determined using the energy integral:

$${\stackrel{}{\stackrel{}{\phi }}}_3^2-3{\cos }^2{\phi }_3={\stackrel{}{\stackrel{}{\phi }}}_2^2-3{\cos }^2{\phi }_2+\Delta h$$.

The challenge is to achieve the end state for a minimum time of pulling. Minimization of time of contraction at constant speed sampling of the cable is adequate to the task of maximizing the angular momentum of rotation of the CCC. The contraction of the CCC is made by the power of the sample cable. Management program retraction in the form of speed sampling of the cable a=const in the angular sector φ₂<φ< & Phi;₃specifies the increment of the energy of rotation in the guise Δh. Transition trajectory described by the system of equations:

$$\frac{d\phi }{d\phi }=1;$$$$\stackrel{}{\stackrel{}{\phi }}\frac{d\stackrel{}{l}}{d\phi }=-a;$$$$\stackrel{}{\stackrel{}{\phi }}\frac{d\stackrel{}{\stackrel{}{\phi }}}{d\phi }=2a\frac{\stackrel{}{\stackrel{}{\phi }}+1}{\stackrel{}{l}}-3\sin \phi \cdot \cos \phi$$.

Come to the optimal control problem with two movable ends: to determine the optimal program of tightening the CCC

a(φ) for φ₂<φ< & Phi;₃and the corresponding transitional trajectory that brings the system from the initial state

end

$${\stackrel{}{\stackrel{}{\phi }}}^2({\phi }_3)-3{\cos }^2{\phi }_3-\Delta h=0$$

at a minimum the length of the selected wire

$$\Delta \stackrel{}{l}=\stackrel{}{l}({\phi }_2)-\stackrel{}{l}({\phi }_3)={\displaystyle \underset{{\phi }_2}{\overset{{\phi }_3}{\int }}\frac{a}{\stackrel{}{\stackrel{}{\phi }}}d\phi }$$.

The Hamiltonian of this system

$$H=\frac{\stackrel{}{u}}{\stackrel{}{\stackrel{}{\phi }}}+{\Psi }_1-{\Psi }_2\frac{\stackrel{}{u}}{\stackrel{}{\stackrel{}{\phi }}}+{\Psi }_3\left(2\frac{a}{\stackrel{}{\stackrel{}{\phi }}}\cdot \frac{\stackrel{}{\stackrel{}{\phi }}+1}{\stackrel{}{l}}-\frac{3}{\stackrel{}{\stackrel{}{\phi }}}\right)$$

linearly dependent on the control. This means that the optimal control is a relay function:

a=const≠0 for φ∈(φ₂that & Phi;₃); and=0 if φ∉(φ₂that & Phi;₃),

and the optimal control problem thus becomes the task performance with edge detection angular sector (φ₂that & Phi;₃) is the sign function switch.

Using the transversality conditions and necessary conditions for an extremum in the form:

$$H^{*}=\underset{u}{\underset{︸}{\max }}H\left({\Psi }^{*},x^{*},a\right);H^{*}({\phi }_2)=H^{*}({\phi }_3)=0$$,

you can solve the boundary problem for the equation

.

This integral can approximately be calculated under conditions allowing to apply theorem on the average:

$$\Delta h=A\left(\ln {\stackrel{}{l}}_1-\ln {\stackrel{}{l}}_3\right)=A\cdot \ln \frac{{\stackrel{}{l}}_1}{{\stackrel{}{l}}_1-\Delta \stackrel{}{l}},$$

where;$${\stackrel{}{\stackrel{}{\phi }}}_{\mathrm{with\; a}p}=\frac{1}{2}\left({\stackrel{}{\stackrel{}{\phi }}}_2+{\stackrel{}{\stackrel{}{\phi }}}_3\right)$$;

$${\stackrel{}{\stackrel{}{\phi }}}_2=\sqrt{3{\cos }^2{\phi }_2}$$;$${\stackrel{}{\stackrel{}{\phi }}}_3=\sqrt{3{\cos }^2({\phi }_2+\Delta \phi )+\Delta h}$$.

This equation establishes a relationship between the change in energy of rotary motion of Δh and resource costs maneuver in the form of a selected length of cable$$\Delta \stackrel{}{l}$$. As can be seen from these relations, resource costs depend on the initial φ₂and the final phase of the sampling cable & Phi;_{3 =φ2+Δφ. This allows the original optimal control problem to minimize the problem of finding the extremum of parametric functions resource costs:}

$${\phi }_2=\underset{{\phi }_2\in ({\phi }_1;-{\phi }_1)}{\arg \min }\left\{\Delta \stackrel{}{l}\left({\phi }_2;\Delta \phi \right)\right\}$$,

where the criterion function

$$\Delta \stackrel{}{l}={\stackrel{}{l}}_1-{\stackrel{}{l}}_3={\stackrel{}{l}}_1(1-\exp (-\Delta h/A))$$

and examined in the extreme. A necessary condition for an extremum gives the equation

$${\stackrel{}{\stackrel{}{\phi }}}_3\cdot \cos {\phi }_2\sin {\phi }_2+{\stackrel{}{\stackrel{}{\phi }}}_2\cdot \cos ({\phi }_2+\Delta \phi )\sin ({\phi }_2+\Delta \phi )=0$$,

the solution of which determines the argument extremum:

$${\phi }_2=\pi -\frac{1}{2}\arctan \frac{\sin 2\Delta \phi }{B(\Delta \phi )+\cos 2\Delta \phi },\text{B}\Delta \phi \text{)}=\sqrt{\text{1}+\frac{\Delta \text{h}}{{\text{3cos}}^{\text{2}}\frac{\Delta \phi }{2}}}$$.

When Δh→0 the summand B(Δφ)→1 and φ₂≈π-0,5·Δφ, that is, the angular sector in the region tightening CCC symmetric with respect to the local vertical of the center of mass in the vicinity of the Zenith and Nadir. With increasing values of the parameter ∆ H symmetry is broken and the sector makes associated offset.

The procedure for solving the problem of translation of the CCC in the rotation mode:

- specify data source: r_with, ΔV, Δh, Δφ;

- calculate the auxiliary parameters:$$\Delta \stackrel{}{V}=\Delta V/V_c,$$ $$V_c=\sqrt{\mu /r_c}$$,$${\omega }_c=\sqrt{\mu /r_c^3,}$$$$T_c=2\pi /{\omega }_c$$;

- determine the motion parameters of the CCC at the end of the deployment:

φ₁=91,5°,$${\stackrel{}{\stackrel{}{\phi }}}_1=0,071$$,$${\stackrel{}{l}}_1=18,4\cdot \Delta \stackrel{}{V}$$;

- define the boundaries of the field of coagulation CCC φ∈(φ₂that & Phi;₂+Δφ);

- determine the average parameter values$${\stackrel{}{\stackrel{}{\phi }}}_{\mathrm{with\; a}p}$$and A;

- calculate the parameters characterizing the process of spin CCC:

1. The relative length of the selected wire$$\Delta \stackrel{}{l}={\stackrel{}{l}}_1(1-\exp (-\Delta h/A))$$.

2. The share of the selected wire after tightening CCC:$$J=\Delta \stackrel{}{l}/{\stackrel{}{l}}_1=1-\exp (-\Delta h/A)$$.

3. The percentage of the selected cable J_h=J/ ∆ H.

4. The sampling time of the rope$$\Delta \stackrel{}{t}=\frac{\Delta \phi }{2\pi \cdot {\stackrel{}{\stackrel{}{\phi }}}_{\mathrm{with\; a}p}}$$.

5. The relative velocity of the sample cable$$a=\frac{\Delta \stackrel{}{l}}{\Delta \phi }{\stackrel{}{\stackrel{}{\phi }}}_{\mathrm{with\; a}p}$$.

6. The end time of the maneuver:

$${\stackrel{}{t}}_3=1,114+\frac{12\pi \sqrt{3}}{}\ln \left(-\frac{1+\sin {\phi }_1}{1+\sin \Delta \phi /2}\cdot \frac{\cos \Delta \phi /2}{\cos {\phi }_1}\right)+\frac{\Delta \phi }{2\pi {\stackrel{}{\stackrel{}{\phi }}}_{\mathrm{with\; a}p}}.$$

The time shall be taken from the moment of allowed objects on the starting orbit. An estimate of the time the maneuver is a half period of the reference orbit of the center of mass.

In Fig.5-8 shows the graphical dependence of the main characteristics of the process of spin CCC. The dependence of the fraction of the selected cable from the increment of the energy of rotation of the CCC (Fig.5) is a clear and objective indicator of the quality of the process under investigation. This quality measure is not sensitive to the size of the sector tightening Δφ, and the value of this index is easy to calculate the radius of rotation of the CCC after its contraction. The percentage of the selected cable when tightening the CCC (Fig.6) is a universal indicator of the effectiveness of the process of spin, as quantitatively determines the resource costs in the form of a length selected Proc. of the sa unit increments the value of the integral energy of rotary motion. The bottom graph in Fig.6 built by the approximate formula:

J_h=Å^-1, Å=18+2,5·Δh, ·Δh≤3. Calculations show that the percentage of the selected cable per unit of energy of rotation when tightening the CCC does not exceed 6%. This is a very high indicator.

In Fig.7 and 8 show plots of the velocity and time of sampling rope for two sizes of the sectors in the field of contraction of the CCC. In Fig.7 shows the graphical dependence of the required speed sampling of the cable in a predetermined angular sector Δφ to translate the CCC in the rotation mode with the energy indicator of Δh. The calculations are performed for the pulse separation ΔV=1 m/s Relative to the sampling time of the cable is proportional to the size of the sector and practically does not depend on the increment value of the integral energy of rotary motion. This is achieved by increasing the speed of the sample cable. This is a very important parameter from the point of view of practical implementation of the process of pulling. Obviously, the power sampling of the cable at high speeds is not the best conditions for operation Executive mechanical devices.

Thus, the possibility of translation of the CCC mode associated rotation by separation and transversal allowed one monolithic object to starting a circular orbit, subsequent passive deployment of the cable to a predetermined length, the translation system is the mode associated pendulum motion with the subsequent contraction of the CCC by the power of the sample cable to switch the system mode associated rotation.

All control inputs to the system are implemented at the expense of its internal forces. The proposed method assumes a rather simple technical feeder-fetch the rope and equally simple program to control this device.

Estimated time to maneuver twist the CCC is a half period of the reference orbit of the center of mass.

Maximum resource costs as the share of the selected cable per unit increment of the energy of rotation when tightening the CCC does not exceed 6%.

References

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The method of deployment and twist tethered space systems (KTS) relative to the center of mass, including undocking and pulse repulsion of the two connected by a cable of interest, the release cable on a given length, the output of the system in the mode associated pendulum motion with the subsequent selection of the wire transfer system in a rotational mode of motion, characterized in that the pulse separation is reported against the orbital velocity vector, when deploying the CCC is a free release rope and translation of the CCC in the rotation mode is mode associated pendulum motion in the angular range of phases φ∈(φ₂that & Phi;₂+Δφ),
where
by sampling the cable is at a constant speed

where Δφ is the angular sector collapse CCC;
- the relative length of the selected wire;
- shows the average angular velocity of the rotational motion of the CCC in the range of angular phases φ∈(φ₂that & Phi;₂+Δφ);
Δh - increment dimensionless integral energy of rotational motion of the CCC.