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Results for “JACOBI INTEGRAL”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Jacobi-Integral Method For Two-Body Problem

Jacobi-integral method enables efficient, accurate computation of trajectory of natural satellite or spacecraft perturbed by component of gravitational potential depending explicitly on both position and time. Instead of total energy, Jacobi integral, which is energylike constant of motion in this case, embedded in Newtonian differential equations of motion. Trajectories computed in fewer steps. With modifications, applicable to such terrestrial problems as motions of rotors and of beams of electrically charged particles in changing electrical and magnetic fields.

Bond, Victor R.↗
NASA NTRS2013

Lyapunov Orbits in the Jupiter System Using Electrodynamic Tethers

Various researchers have proposed the use of electrodynamic tethers for power generation and capture from interplanetary transfers. The effect of tether forces on periodic orbits in Jupiter-satellite systems are investigated. A perturbation force is added to the restricted three-body problem model and a series of simplifications allows development of a conservative system that retains the Jacobi integral. Expressions are developed to find modified locations of equilibrium positions. Modified families of Lyapunov orbits are generated as functions of tether size and Jacobi integral. Zero velocity curves and stability analyses are used to evaluate the dynamical properties of tether-modified orbits.

Cassini↗
NASA NTRS1976

The evolution of comet orbits

The origin of comets and the evolution of their orbits are discussed. Factors considered include: the law of survival of comets against ejection on hyperbolic orbits; short-period comets are not created by single close encounters of near-parabolic comets with Jupiter; observable long-period comets do not evolve into observable short-period comets; unobservable long-period comets with perihelia near Jupiter can evolve into observable short-period comets; long-period comets cannot have been formed or created within the planetary region of the solar system (excluding the effects of stellar perturbations); it is possible that some of the short-period comets could have been formed inside the orbit of Neptune; circularly-restricted three-body problem, and its associated Jacobi integral, are not valid approximations to use in studying origin and evolution of comets.

Everhart, E.↗
NASA NTRS1980

Life near the Roche limit - Behavior of ejecta from satellites close to planets

A study of the dynamics of nearby debris from impact craters was made to explain the distinctive features seen on Phobos, Deimis, and Amalthea. The planetary tides and satellite rotation were considered, and the usual pseudo-energy (Jacobi) integral was numerically calculated in the framework of a restricted body problem where satellites are modelled as triaxial ellipsoids rather than point masses. Iso-contours of this integral show that Deimos and Amalthea are entirely closed by Roche lobes, and the surfaces of their model ellipsoids lie nearly along equipotentials. Presently, the surface of Phobos overflows its Roche lobe, except for regions within a few km of the sub-Mars and anti-Mars points. The behavior of crater ejecta from the satellites of Mars were also examined by numerical integration of trajectories for particles leaving their surfaces in the equatorial plane.

Dobrovolskis, A. R.↗
NASA NTRS1980

Motion about the stable libration points in the linearized, restricted three-body problem

The motion of a point particle in the neighborhood of a triangular libration point (L sub 4 or L sub 5) in the linearized, restricted problem of three bodies in the plane is described. The derivation of the equations of motion is standard. From these equations, three invariants of the motion are obtained; the Jacobi integral is expressed linearly in terms of two of these. The trajectories for varied initial conditions are drawn, and a complete geometric description of the particle motion is given in elementary terms. Each trajectory has an exterior boundary curve; its equation is found. An approximation to this boundary curve was known; the two curves are compared graphically. For certain initial conditions, there is an interior region from which the trajectory is excluded; the equation of the boundary of this region is given.

Mittleman, D.↗
NASA NTRS1996

Orbits Close to Asteroid 4769 Castalia

We use a radar-derived physical model of 4769 Castalia (1989 PB) to investigate close orbit dynamics around that kilometer- sized, uniformly rotating asteroid. Our methods of analysis provide a basis for systematic studies of particle dynamics close to any uniformly rotating asteroid. We establish that a Jacobi integral exists for particles orbiting this asteroid, examine the attendant zero-velocity surfaces, find families of periodic orbits, and determine their stability. All synchronous orbits and direct orbits within approx. 3 mean radii of Castalia are unstable and are subject to impact or escape from Castalia. Retrograde orbits are mostly stable and allow particles to orbit close to the asteroid surface. We derive a model which allows us to predict the escape conditions of a particle in orbit about Castalia and the (temporary) capture conditions for a hyperbolic interloper. Orbits within 1.5 km of Castalia are subject to immediate ejection from the system. Hyperbolic orbits with a V(sub infinity) less than 0.4 m/sec can potentially be captured by Castalia if their periapsis radius Is within approx. 2 km. For Castalia this capture region is small, but the results also apply to larger asteroids whose capture regions would also be larger. We determine bounds on ejecta speeds which either ensure ejecta escape or re-impact as functions of location on Castalia's surface. The speeds that ensure escape range from 0.28 to 0.84 m/sec and the speeds that ensure re-impact range from 0 to 0.18 m/sec. Speeds between these two bounds lead either to escape, re-impact, or potentially finite-time stable orbits. We develop a simple criterion which can establish whether a particle could have been ejected from the asteroid in the past and if it will impact the surface in the future.

Scheeres, D. J.↗
NASA NTRS2003

Lunar transfer trajectory design and the four-body problem

The existence of a ballistic trajectory from the Earth to orbit about the Moon was long considered to be impossible based on analysis of the three-body problem. In 1990 a ballistic trajectory from the Earth to lunar orbit was discovered while analyzing a plan to salvage the Muses A (Hiten) spacecraft. This trajectory utilized the Sun's gravity in conjunction with the Earth and Moon's gravity and was thus the first example of a practical four-body trajectory design. This paper presents a review of lunar transfer trajectories that go beyond three-body theory and the Jacobi integral. These include Hiten, Lunar A and the Genesis return trajectory from the vicinity of the Moon to Earth.It is shown that these trajectories may be analyzed by piecing together segments where three-body motion dominates.

Muses↗
NASA NTRS1995

Orbits Close to Asteroid 4769 Castalia

We use a radar-derived physical model of the kilometer sized, uniformly rotating asteroid 4769 Castalia (1989 PB) to investigate close orbit dynamics. We establish that a Jacobi integral exists for particles orbiting this asteroid, and the attendant zero-velocity surfaces are generated and examined. We find families of periodic orbits and determine their stability. We find that all synchronous orbits and direct orbits within 3 mean radii of Castalia are unstable and are subject to impact or escape from Castalia. We find that retrograde orbits are mostly stable and allow particles to orbit closely to the asteroid surface.

Asteroid↗
DOE OSTI2025

Quantum Hamilton-Jacobi theory, spectral path integrals, and exact WKB analysis

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi (HJ) theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in quantum theory beyond approximation schemes. The canonical transformation enables one to set the new Hamiltonian to constant or zero, but keeps the information about solution in Hamilton’s characteristic function. To benefit from this in quantum theory, one must work with a formulation in which classical Hamiltonian is used. This uniquely points to phase space path integral. However, the main variable in HJ formalism is energy, not time. Thus, we are led to consider the Fourier transform of the path integral, the spectral path integral Z ˜ ( E ) . The evaluation of path integrals reduces to determining the quantum Hamilton characteristic functions (which can be achieved via an asymptotic analysis) and a discrete sum over the quantum period lattice, generalizing Gutzwiller’s sum. Published by the American Physical Society 2025

Türe, Mustafa (ORCID:0009000975968618)↗
NASA NTRS1965

Notes on the restricted three body problem- approximate behavior of solutions near the collinear lagrangian points

Studies the solutions of the restricted three-body problem near those equilibrium points which are collinear with the two positive masses. This is done to gain insight toward the development of an analytic proof and classification of the periodic orbits that pass near these equilibrium points, which have been discovered numerically by M. Davidson, and also to hopefully gain insight into the nature of solutions of the restricted three-body problem in general. The qualitative observations that are made are all deduced from the linearized equations.

Approximation method↗