The potential energy of a small rigid body in the gravitational field of an oblate spheroid

Roberson, Robert E.; Tatistcheff, D.

doi:10.1016/0016-0032(56)90560-9

Cited by 25 publications

(7 citation statements)

References 3 publications

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“…(12-14) below. These expressions are extremely simple and involve only the eigenvalues of the gravitational gradient tensor and the eigenvalues of the body inertia tensor [7] with respect to a reference point 0. Since they are applicable to any gravitational field and any rigid body, and do not depend on small-angle approximations, the results are of general theoretical interest.…”

Section: Gravitational Gradient Torques On a Rigid Bodymentioning

confidence: 99%

A new approach to gravitational gradient determination of the vertical

Diesel¹

1964

AIAA Journal

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A new technique is described for accurately determining the vertical from orbiting vehicles. Although the gravitational gradient phenomenon on which it is based is already well known, previously proposed devices based on this effect are impractical because of inherent accelerometer errors and extraneous vehicle motion that would disturb the accelerometer case. The new approach described herein bypasses both of these problems. The proposed system is unaffected by bias and scale factor errors and senses only the desired gravitational differences even when not in free fall. To explain the approach, a general theory of the gravitational gradient effect is presented. It is shown that the directions defined by this effect are the eigenvectors of a second-rank tensor. These eigenvectors are then determined for the earth's gravitational field, and a simple new method of finding the gravitational torques on rigid bodies is presented. Finally, some general results are obtained regarding the effect of the gravitational gradient on the constrained motion of rigid bodies such as would be used in this approach.

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Section: Gravitational Gradient Torques On a Rigid Bodymentioning

confidence: 99%

A new approach to gravitational gradient determination of the vertical

Diesel¹

1964

AIAA Journal

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“…8 In general, B may range from 0°to 360°. All quadrant ambiguities presented by (10) are resolved by noting the algebraic signs of (9) and (9a).…”

Section: Construction Of the Locus Circlementioning

confidence: 99%

Attitude Determination and Prediction of Spin-Stabilized Satellites

Thomas¹,

Cappellari²

1964

Bell System Technical Journal

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“…A major advantage of this choice is that some perturbation torques (e.g., the gravitational torque discussed in [4] and inertial reaction torques) are most naturally expressed in terms of a principal axis system. Moreover, these axes are often close to axes of physical symmetry of the vehicle, which are the natural reference frame for still other perturbation torques.…”

Section: Attitude Deviation Anglesmentioning

confidence: 99%

“…It is known [4] that an attitude perturbation torque arises from the gravitational field of the earth tending to line the satellite up with its long axis normal to the local gravitational equipotential surface. Moreover, it can be shown that this can be a significant, if not major, torque source.…”

Section: Attitude Reference Systemsmentioning

confidence: 99%

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Attitude Control of a Satellite Vehicle—an Outline of the Problems

Roberson¹

1958

VIIIth International Astronautical Congress Barcelona 1957 / VIII. Internationaler Astronautischer Kongress / VIIIe Congrès Int

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-Zusammenfassung -ResurneAttitude Control of a Satellite Vehicle -an Outline of the Problems. The attitude of a satellite vehicle must be controlled for many applications. This paper describes some of the fundamental problems associated with the design of an attitude control system. These include the choice of an attitude reference system and of reference axes within the body, and the nature of the attitude perturbation torques acting on the satellite. Attitude equations of motion are derived and a rationale for a control system synthesis is suggested. Control torque sources, the effects of vehicle configuration, and the role of attitude sensing devices are discussed.

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The potential energy of a small rigid body in the gravitational field of an oblate spheroid

Cited by 25 publications

References 3 publications

A new approach to gravitational gradient determination of the vertical

A new approach to gravitational gradient determination of the vertical

Attitude Determination and Prediction of Spin-Stabilized Satellites

Attitude Control of a Satellite Vehicle—an Outline of the Problems

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