Time-fixed rendezvous by impulse factoring with an intermediate timing constraint

A method is presented for factoring a two-impulse orbital transfer into a three- or four-impulse transfer which solves the rendezvous problem and satisfies an intermediate timing constraint. Both the time of rendezvous and the intermediate time of a alinement are formulated as any element of a finite sequence of times. These times are integer multiples of a constant plus an additive constant. The rendezvous condition is an equality constraint, whereas the intermediate alinement is an inequality constraint. The two timing constraints are satisfied by factoring the impulses into collinear parts that vectorially sum to the original impulse and by varying the resultant period differences and the number of revolutions in each orbit. Five different types of solutions arise by considering factoring either or both of the two impulses into two or three parts with a limit for four total impulses. The impulse-factoring technique may be applied to any two-impulse transfer which has distinct orbital periods

Determination of ASPS performance for large payloads in the shuttle orbiter disturbance environment

A high fidelity simulation of the annular suspension and pointing system (ASPS), its payload, and the shuttle orbiter was used to define the worst case orientations of the ASPS and its payload for the various vehicle disturbances, and to determine the performance capability of the ASPS under these conditions. The most demanding and largest proposed payload, the Solar Optical Telescope was selected for study. It was found that, in all cases, the ASPS more than satisfied the payload's requirements. It is concluded that, to satisfy facility class payload requirements, the ASPS or a shuttle orbiter free-drift mode (control system off) should be utilized

In memoriam two distinguished participants of the Bregenz Symmetries in Science Symposia: Marcos Moshinsky and Yurii Fedorovich Smirnov

Some particular facets of the numerous works by Marcos Moshinsky and Yurii Fedorovich Smirnov are presented in these notes. The accent is put on some of the common interests of Yurii and Marcos in physics, theoretical chemistry, and mathematical physics. These notes also contain some more personal memories of Yurii Smirnov.Comment: Submitted for publication in Journal of Physics: Conference Serie

Modification of an impulse-factoring orbital transfer technique to account for orbit determination and maneuver execution errors

A method has previously been developed to satisfy terminal rendezvous and intermediate timing constraints for planetary missions involving orbital operations. The method uses impulse factoring in which a two-impulse transfer is divided into three or four impulses which add one or two intermediate orbits. The periods of the intermediate orbits and the number of revolutions in each orbit are varied to satisfy timing constraints. Techniques are developed to retarget the orbital transfer in the presence of orbit-determination and maneuver-execution errors. Sample results indicate that the nominal transfer can be retargeted with little change in either the magnitude (Delta V) or location of the individual impulses. Additonally, the total Delta V required for the retargeted transfer is little different from that required for the nominal transfer. A digital computer program developed to implement the techniques is described

Sum Rules for Multi-Photon Spectroscopy of Ions in Finite Symmetry

Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity- forbidden p-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models.Comment: 16 pages, Tex fil

On the use of the group SO(4,2) in atomic and molecular physics

In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little groups. The second approach is by a new symmetry descent process starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional harmonic oscillator. It is based on the little known concept of a Lie algebra under constraints and corresponds in some sense to a symmetry breaking mechanism. This paper ends with a brief discussion of the interest of SO(4,2) for a new group-theoretical approach to the periodic table of chemical elements. In this connection, a general ongoing programme based on the use of a complete set of commuting operators is briefly described. It is believed that the present paper could be useful not only to the atomic and molecular community but also to people working in theoretical and mathematical physics.Comment: 31 page

Obtainment of internal labelling operators as broken Casimir operators by means of contractions related to reduction chains in semisimple Lie algebras

We show that the In\"on\"u-Wigner contraction naturally associated to a reduction chain $\frak{s}\supset \frak{s}^{\prime}$ of semisimple Lie algebras induces a decomposition of the Casimir operators into homogeneous polynomials, the terms of which can be used to obtain additional mutually commuting missing label operators for this reduction. The adjunction of these scalars that are no more invariants of the contraction allow to solve the missing label problem for those reductions where the contraction provides an insufficient number of labelling operators

Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems

We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define an (Hamiltonian) operator associated with A(k) and examine the degeneracies of its spectrum. For the finite (when k < 0) and the infinite (when k > 0 or = 0) representations of A(k), we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators. To overcome the difficulties related to the phase operator in the infinite-dimensional case and to avoid the degeneracy problem for the finite-dimensional case, we introduce a truncation procedure which generalizes the one used by Pegg and Barnett for the harmonic oscillator. This yields a truncated generalized oscillator algebra A(k,s), where s denotes the truncation order. We construct two types of temporally stable states for A(k,s) (as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of A(k,s)). Two applications are considered in this article. The first concerns physical realizations of A(k) and A(k,s) in the context of one-dimensional quantum systems with finite (Morse system) or infinite (Poeschl-Teller system) discrete spectra. The second deals with mutually unbiased bases used in quantum information.Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretical as a pape

On the construction of generalized Grassmann representatives of state vectors

Generalized $Z_k$-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors.Comment: 8 page