10 Thruster Rotation Angle Control During Contactless Removal …
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thrust P I generated by IB, when the entire wedge-shaped beam reaches SDO, on the
relative range L and the IB divergence angle β I is taken as Eq. 10.4.
P TN =
P I
R T ≤ L × tg(β I )
P I ×R T
L×tg(β I )
R T > L × tg(β I )
(10.4)
Due to a certain degree of approximation of the proposed dependences, it is
assumed here that IB has a uniform angular distribution of ion flow density.
During the SDO rotation due to various factors, the components of the force of the
IB impact on SDO arise in a plane orthogonal to the relative range direction. In the
simulation model, it is proposed to use a harmonic law to describe these forces also,
and the magnitude of such forces is assumed to be proportional to the force acting in
the direction of relative range. The components of the lateral forces are defined by
Eq. 10.5.
P T V i = P TN × k V i × sin
φ V i +
2π
T V i
× t
(10.5)
Here, i designates the values of X and Z, k V i is the ratio of the maximum value
of the lateral force component to the magnitude of the force acting in the direction
of relative range, and φ V i , T V i are the phase shift and the period of the oscillatory
lateral force of IB impact on SDO.
10.5 Simulation of Spacecraft Motion Dynamics
For spacecraft motion dynamics simulation, spacecraft motion equations and their
integration results are presented in Sect. 10.5.1. The dynamics of spacecraft-SDO
relative distance is described in Sect. 10.5.2. The angles of the thruster rotation
examples in SDO removal are demonstrated in Sect. 10.5.3.
10.5.1 Integration of Motion Equations
Numerical simulation was performed to assess the possibility of controlling SDO
transportation into the disposal orbit using the pivoted thrusters of EPS. The equations
of the SSC motion and SDO motion relative to SSC were considered in a geocentric
inertial coordinate system without taking into account disturbances from the nonsphericity of the Earth and disturbing factors of a higher order of smallness. The
integration duration was up to 3 days.
The following data were used. The initial SDO position was set by the parameters
of the elliptical orbit: the semimajor axis 42,157 km, the eccentricity 0.0005, and
133
thrust P I generated by IB, when the entire wedge-shaped beam reaches SDO, on the
relative range L and the IB divergence angle β I is taken as Eq. 10.4.
P TN =
P I
R T ≤ L × tg(β I )
P I ×R T
L×tg(β I )
R T > L × tg(β I )
(10.4)
Due to a certain degree of approximation of the proposed dependences, it is
assumed here that IB has a uniform angular distribution of ion flow density.
During the SDO rotation due to various factors, the components of the force of the
IB impact on SDO arise in a plane orthogonal to the relative range direction. In the
simulation model, it is proposed to use a harmonic law to describe these forces also,
and the magnitude of such forces is assumed to be proportional to the force acting in
the direction of relative range. The components of the lateral forces are defined by
Eq. 10.5.
P T V i = P TN × k V i × sin
φ V i +
2π
T V i
× t
(10.5)
Here, i designates the values of X and Z, k V i is the ratio of the maximum value
of the lateral force component to the magnitude of the force acting in the direction
of relative range, and φ V i , T V i are the phase shift and the period of the oscillatory
lateral force of IB impact on SDO.
10.5 Simulation of Spacecraft Motion Dynamics
For spacecraft motion dynamics simulation, spacecraft motion equations and their
integration results are presented in Sect. 10.5.1. The dynamics of spacecraft-SDO
relative distance is described in Sect. 10.5.2. The angles of the thruster rotation
examples in SDO removal are demonstrated in Sect. 10.5.3.
10.5.1 Integration of Motion Equations
Numerical simulation was performed to assess the possibility of controlling SDO
transportation into the disposal orbit using the pivoted thrusters of EPS. The equations
of the SSC motion and SDO motion relative to SSC were considered in a geocentric
inertial coordinate system without taking into account disturbances from the nonsphericity of the Earth and disturbing factors of a higher order of smallness. The
integration duration was up to 3 days.
The following data were used. The initial SDO position was set by the parameters
of the elliptical orbit: the semimajor axis 42,157 km, the eccentricity 0.0005, and