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Nacozy, P. E.

Publications and source records attributed to Nacozy, P. E..

14 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Periodic orbits of the general three-body problem for the sun-Jupiter-Saturn system

Two families of symmetric periodic orbits of the planar, general, three-body problem are presented. The masses of the three bodies include ratios equal to the sun-Jupiter-Saturn system and the periods of the orbits of Jupiter and Saturn are in a 2:5 resonance. The (linear) stability of the orbits are studied in relation to eccentricity and mass variations. The generation of the two families of periodic orbits follows a systematic approach and employs (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to the elliptic restricted problem and from the circular and elliptic problems to the general problem through bifurcation phenomena relating the three dynamical systems. The approach also provides insight into the evolutionary process of periodic orbits continued from the restricted problems to the general problem.

Kwok, J. H.↗
NASA NTRS1984

Dynamics analysis of electrodynamic satellite tethers. Equations of motion and numerical solution algorithms for the tether

The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.

Nacozy, P. E.↗
NASA NTRS1982

Long-term motion of resonant satellites with arbitrary eccentricity and inclination

A first-order, semi-analytical method for the long-term motion of resonant satellites is introduced. The method provides long-term solutions, valid for nearly all eccentricities and inclinations, and for all commensurability ratios. The method allows the inclusion of all zonal and tesseral harmonics of a nonspherical planet. We present here an application of the method to a synchronous satellite including J2 and J22 harmonics. Global, long-term solutions for this problem are given for arbitrary values of eccentricity, argument of perigee and inclination.

Nacozy, P. E.↗
NASA NTRS1982

Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system

A systematic approach to generate periodic orbits in the elliptic restricted problem of three bodies is introduced. The approach is based on (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to periodic orbits in the elliptic restricted problem. Two families of periodic orbits of the elliptic restricted problem are found by this approach. The mass ratio of the primaries of these orbits is equal to that of the Sun-Jupiter system. The sidereal mean motions between the infinitesimal body and the smaller primary are in a 2:5 resonance, so as to approximate the Sun-Jupiter-Saturn system. The lineaar stabilities of these periodic orbits are studied as functions of the eccentricities of the primaries and of the infinitesimal body. The results show that both stable and unstable periodic orbits exist in the elliptic restricted problem that are close to the actual Sun-Jupiter-Saturn system. However, the periodic orbit closest to the actual Sun-Jupiter-Saturn system is (linearly) stable.

Kwok, J. H.↗
NASA NTRS1981

Time elements in Keplerian orbital elements

Time elements are introduced in terms of Keplerian (classical) orbital elements for use with time transformations of the Sundman type. Three different time elements are introduced. One time element is associated with the eccentric anomaly, a second time element is associated with the true anomaly, and a third time element is associated with the intermediate anomaly. Numerical results are presented that show accuracy improvements of from one to two orders of magnitude when time elements are employed along with Sundman time transformations, compared with using time transformations alone.

Nacozy, P. E.↗
NASA NTRS1978

A semianalytical theory for the long-term motion of Pluto

The semianalytical approach to long-term solutions of resonant systems with three degrees of freedom, proposed by Giacaglia in 1965, is used to study the long-term motion of Pluto. The study takes into account the effects of Jupiter, Saturn and Uranus on the motion of Pluto. Modified periodic orbits of the third kind constitute the solutions; Pluto is found to librate about one of these periodic solutions. The long-term eccentricity, inclination, perihelion and librational amplitude of the planet are discussed.

Nacozy, P. E.↗
NASA NTRS1978

A discussion of the solution for the motion of Pluto

The semianalytical solution for Pluto given by Nacozy and Diehl (1978) is compared with the numerical solution obtained by Williams and Benson (1971). The effect of the Pluto-Uranus near resonance is discussed along with how it can be incorporated into the solution. Details are given on the calculation of certain quantities in the long-term solution. A calculation of librational periods of the perihelion, eccentricity, and inclination is performed. The calculation is based on the method of Giacaglia and Hori (1968).

Nacozy, P. E.↗
NASA NTRS1977

The geopotential in nonsingular orbital elements

Singularities are eliminated from the geopotential and its partial derivatives for zero eccentricity and inclination, and an expression for the geopotential expansion based entirely on nonsingular orbital elements is developed. The argument relies on the treatments of the geopotential function given by Izsak (1964), Allan (1965) and Kaula (1966); the geopotential expansion developed does not involve mixed variables, and therefore does not require the chain rule to formulate the Lagrange planetary equations. The need for recursion relations to be used in conjunction with the nonsingular version of the geopotential expansion is also mentioned.

Nacozy, P. E.↗
NASA NTRS1975

Solutions of the motion of synchronous satellites with arbitrary eccentricity and inclination

A first order, semianalytical theory for the long term motion of resonant satellites is presented. The theory is valid for all eccentricities and inclinations and for all commensurability ratios. The method allows the inclusion of all the zonal and tesseral harmonics as well as luni solar perturbations and radiation pressure. The method is applied to a synchronous satellite including only the J sub 2 and J sub 22 harmonics. Global, long term solutions for this problem, eccentricity, argument of perigee, and inclination are obtained.

Nacozy, P. E.↗
NASA NTRS1975

Time elements

Time elements are introduced for use with Sundman time transformations for satellite equations of motion. Two time elements are presented, one providing maximum accuracy when the exponent of the governing equation equals 1, the other when the exponent equals 2. Time elements and time transformations reduce local truncation error and Liapunov (in-track) instability, and provide analytical step size control. Numerical results show accuracy improvements of more than one order of magnitude when time elements are employed with time transformations in the numerical integration of the satellite equations, compared with using time transformations alone.

Nacozy, P. E.↗
NASA NTRS1974

Time elements

Time elements are introduced for use with Sundman time transformations of the type dt = r(alpha)ds for satellite equations of motion. Two time elements are given, one providing maximum accuracy for alpha = 1, the other for alpha = 2. Time elements and time transformations reduce local truncation error and Liapunov (in track) instability, and provide analytical step size control. Numerical results show accuracy improvements of more than one order of magnitude when time elements are employed with time transformations in the numerical integration of the satellite equations, compared with using time transformations alone.

Nacozy, P. E.↗
NASA NTRS1974

Investigation of highly efficient satellite solution methods

Methods for analyzing the stability of satellites are discussed. The subjects considered are: (1) time elements, (2) stabilization by external energy corrections, and (3) long term global solutions for the synchronous satellite. A set of canonical two-body elements referred to as Delaunay-similar elements is presented. In contrast to the classical Delaunay theory which has time as the independent variable, the D-S theory uses an independent variable which is a generalized true anomaly. The numerical integration of the canonical perturbation equations of these elements is developed.

Nacozy, P. E.↗
NASA NTRS1973

The Lyapunov stabilization of satellite equations of motion using integrals

A method is introduced that weakens the Lyapunov or in track instability of satellite equations of motion. The method utilizes a linearized energy integral of satellite motion as a constraint on solutions obtained by numerical integration. The procedure prevents local numerical error from altering the frequency associated with the fast angular variable and thereby reduces the Lyapunov instability and the global numerical error. Applications of the method to satellite motion show accuracy improvements of two to three orders of magnitude in position and velocity after 50 revolutions. A modification of the method is presented that allows the use of slowly varying integrals of motion.

Nacozy, P. E.↗