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Fitzpatrick, P. M.

Publications and source records attributed to Fitzpatrick, P. M..

11 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

Hoots, F. R.↗
NASA NTRS1975

Poisson equations of rotational motion for a rigid triaxial body with application to a tumbling artificial satellite

A mathematical model is developed for studying the effects of gravity gradient torque on the attitude stability of a tumbling triaxial rigid satellite. Poisson equations are used to investigate the rotation of the satellite (which is in elliptical orbit about an attracting point mass) about its center of mass. An averaging method is employed to obtain an intermediate set of differential equations for the nonresonant, secular behavior of the osculating elements which describe the rotational motions of the satellite, and the averaged equations are then integrated to obtain long-term secular solutions for the osculating elements.

Liu, J. J. F.↗
NASA NTRS1974

Some suggested approaches to solving the Hamilton-Jacobi equation associated with constrained rigid body motion

Some methods of approaching a solution to the Hamilton-Jacobi equation are outlined and examples are given to illustrate particular methods. These methods may be used for cases where the Hamilton-Jacobi equation is not separable and have been particularly useful in solving the rigid body motion of an earth satellite subjected to gravity torques. These general applications may also have usefulness in studying the motion of satellites with aerodynamic torque and in studying space vehicle motion where thrusting is involved.

Fitzpatrick, P. M.↗
NASA NTRS1974

Hamilton/Jacobi perturbation methods applied to the rotational motion of a rigid body in a gravitational field

The formalism for studying perturbations of a triaxial rigid body within the Hamilton-Jacobi framework is developed. The motion of a triaxial artificial earth satellite about its center of mass is studied. Variables are found which permit separation, and the Euler angles and associated conjugate momenta are obtained as functions of canonical constants and time.

Fitzpatrick, P. M.↗
NASA NTRS1973

Further comments on the application of the method of averaging to the study of the rotational motions of a triaxial rigid body, part 3

Variational equations were applied to the case of a rapidly spinning triaxial body moving in an elliptic orbit, in which the orbital plane is regressing at a constant rate. The explicit differential equations obtained in this application were integrated by the method of averaging to develop secular analytical expressions, which, to first-order in a small parameter, describe the complete space motions of the rigid body under the influence of nonresonant gravity-gradient perturbations. The effects of aerodynamic torque on the rotational motion of an orbiting satellite are studied, as another example of the application of the variational equations derived and the method of averaging.

Liu, J. J. F.↗
NASA NTRS1970

Principles of celestial mechanics

Book on celestial mechanics covering perturbation methods, two body problems, astronomical coordinates, orbital mechanics, satellite rotation, gravitational effects, etc

Fitzpatrick, P. M.↗