Gravitational excitation of an extensible dumbbell satellite.

Chobotov, V. A.

doi:10.2514/3.29074

Cited by 22 publications

(7 citation statements)

References 4 publications

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“…A detailed analysis for this case is given in Ref . 8 and also in Ref . 10 and, therefore, will not be repeated here.…”

Section: Single Mass Modelmentioning

confidence: 92%

“…7 ' 8 The present work considers a similar problem to that posed by Chobotov in Ref. 8 but includes additional aspects of the problem not considered in Ref. 8.…”

Section: Introductionmentioning

confidence: 95%

“…8 but includes additional aspects of the problem not considered in Ref. 8. In particular, certain effects encountered in elliptical orbits are examined, some specific numerical solutions of the nonlinear equations are presented, and a different stability analysis is reported.…”

Section: Introductionmentioning

confidence: 99%

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Motion and stability of a spinning spring-mass system in orbit.

Crist

Eisley

1969

Journal of Spacecraft and Rockets

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Equations are derived for the motion of an elastic dumbbell satellite and a satellite consisting of a small mass connected by a spring to a central body or very large mass. The stability of spinning motion is investigated both from energy considerations and by Floquet theory. Numerical solutions are obtained for the motion which confirm the stability analyses and show typical behavior in a region of practical interest.

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“…A detailed analysis for this case is given in Ref . 8 and also in Ref . 10 and, therefore, will not be repeated here.…”

Section: Single Mass Modelmentioning

confidence: 92%

“…7 ' 8 The present work considers a similar problem to that posed by Chobotov in Ref. 8 but includes additional aspects of the problem not considered in Ref. 8.…”

Section: Introductionmentioning

confidence: 95%

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Motion and stability of a spinning spring-mass system in orbit.

Crist

Eisley

1969

Journal of Spacecraft and Rockets

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“…The kinetic energy of the sensor in a circular orbit is given by T = i(7 0 0 2 + m^j 2 + m 0 r 2 2 ) (7) where co 0 = (^/P 3 ) 1/2 is the orbital angular velocity, and 0 = 0 ; + co 0 .…”

Section: Equations Of Motionmentioning

confidence: 99%

Radially vibrating, rotating gravitational gradient sensor.

Chobotov

1968

Journal of Spacecraft and Rockets

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The concept and operating characteristics of a radially vibrating, gravitational gradient sensor are presented. The sensor is a tuned mechanical oscillator that responds to gravitygradient forces when it is rotated in a stationary gravitational field. Because of the inherent dynamic magnification resulting from resonant or near-resonant operation of the sensor it obtains high sensitivity and can potentially be used as an accurate attitude control sensor, an orbital altimeter, or a navigation aid in a variety of satellite applications. Nomenclature A= nondimensional amplitude C = sensor disk or tube polar inertia AT" = C/mro* = sensor inertia parameter /o = instantaneous inertia of sensor Q r -generalized dissipative force c = viscous damping coefficient k = sensor spring constant I = free length of spring n = damping factor -\ r = n + r 2 = sensor axial coordinate I = time u -test mass displacement from equilibrium x = r/ro = 1 + u/r 0 = 1 + y y = M/r 0 z =' y -o>o 2 /2o>n 2 c c -critical viscous damping coefficient Wo = sensor and satellite mass mi = sensor test mass r 0 = equilibrium length of spring at 0 = ft = constant r lt r 2 = distances as defined in Fig. 1 m = ra 0 Wi/(7??o + mi) = reduced system mass A A = 12 -w 0 $ = phase angle 12 = predominant (constant) absolute angular velocity of the sensor f = c/c c , damping ratio /u = earth's gravitational constant i f / = oscillatory angular displacement about an average value of 0' PL -distances as defined in Fig. 1; i = 1,2 co 0 = orbital angular velocity ton = sensor natural frequency in a gravitational field co r .-sensor natural frequency at rest (0 = 0) ov = undamped natural frequency of the sensor 0,0 ~ sensor absolute angular displacement and rate, respectively 0', 0' = sensor angular displacement and rate, respectively, relative to local vertical 0'av = ft -o>o = average value of angular velocity relative to the local vertical

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“…The spinning motion of the system was confined to the orbital plane, and numerical simulations were used to analyze the system dynamics. Chobotov (1967) studied a spinning TSS by modeling the system as two point masses connected by a massless linear spring. The system mass center remained on an unperturbed circular orbit and the motion of the system was confined to the orbital plane.…”

Section: Introductionmentioning

confidence: 99%

Out-of-plane librations of spinning tethered satellite systems

Ellis

Hall

2009

Celest Mech Dyn Astr

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We analyze the out-of-plane librations of a tethered satellite system that is nominally rotating in the orbit plane. To isolate the librational dynamics, the system is modeled as two point masses connected by a rigid rod with the system mass center constrained to an unperturbed circular orbit. For small out-of-plane librations, the in-plane motion is unaffected by the out-of-plane librations and a solution for the in-plane motion is determined in terms of Jacobi elliptic functions. This solution is used in the linearized equation for the out-of-plane librations, resulting in a Hill's equation. Floquet theory is used to analyze the Hill's equation, and we show that the out-of-plane librations are unstable for certain ranges of in-plane spin rate. For relatively high in-plane spin rates, the out-of-plane librations are stable, and the Hill's equation can be approximated by a Mathieu's equation. Approximate solutions to the Mathieu's equation are determined, and we analyze the dominant characteristics of the out-of-plane librations for high in-plane spin rates. The results obtained from the analysis of the linearized equations of motion are compared to numerical simulations of the nonlinear equations of motion, as well as numerical simulations of a more realistic system model that accounts for tether flexibility. The instabilities discovered from the linear analysis are present in both the nonlinear system and the more realistic system model. The approximate solutions for the out-of-plane librations compare well to the nonlinear system for relatively high in-plane rotation rates, and also capture the significant qualitative behavior of the flexible system.

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Gravitational excitation of an extensible dumbbell satellite.

Cited by 22 publications

References 4 publications

Motion and stability of a spinning spring-mass system in orbit.

Motion and stability of a spinning spring-mass system in orbit.

Radially vibrating, rotating gravitational gradient sensor.

Out-of-plane librations of spinning tethered satellite systems

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