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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Hamiltonian cosmology.

The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.

Ryan, M.↗
NASA NTRS1976

New treatment of the critical argument in resonance problems

Traditional methods for isolating the critical argument in Hamiltonian mechanics involve the introduction of a special set of action variables which are both complicated in form and arbitrary in nature. The new variables are in general obscure in their interpretation. This paper introduces a new canonical system corresponding to the original one, but with one more degree of freedom, in which all the variables of the original Hamiltonian can be treated on the same footing. It appears to have significant advantages for machine calculations.

Jefferys, W. H.↗
NASA NTRS1981

Canonical orbital elements in terms of an arbitrary independent variable

Within the framework of the Hamiltonian mechanics in the extended phase space, a set of canonical elements of the Delaunay type is developed in terms of an arbitary independent angular variable. Application to the four classical anomalies - eccentric, true, elliptic, and mean - is presented. Particular attention is given to the generalized time equation and its conjugate energy equation.

Bond, V. R.↗
NASA NTRS1993

Proper-time relativistic dynamics

Proper-time relativistic single-particle classical Hamiltonian mechanics is formulated using a transformation from observer time to system proper time which is a canonical contact transformation on extended phase space. It is shown that interaction induces a change in the symmetry structure of the system which can be analyzed in terms of a Lie-isotopic deformation of the algebra of observables.

Gill, Tepper L.↗
NASA NTRS2002

Microwave, Millimeter, Submillimeter, and Far Infrared Spectral Databases

The spectrum of most known astrophysical molecules is derived from transitions between a few hundred to a few hundred thousand energy levels populated at room temperature. In the microwave and millimeter wave regions. spectroscopy is almost always performed with traditional microwave techniques. In the submillimeter and far infrared microwave technique becomes progressively more technologically challenging and infrared techniques become more widely employed as the wavelength gets shorter. Infrared techniques are typically one to two orders of magnitude less precise but they do generate all the strong features in the spectrum. With microwave technique, it is generally impossible and rarely necessary to measure every single transition of a molecular species, so careful fitting of quantum mechanical Hamiltonians to the transitions measured are required to produce the complete spectral picture of the molecule required by astronomers. The fitting process produces the most precise data possible and is required in the interpret heterodyne observations. The drawback of traditional microwave technique is that precise knowledge of the band origins of low lying excited states is rarely gained. The fitting of data interpolates well for the range of quantum numbers where there is laboratory data, but extrapolation is almost never precise. The majority of high resolution spectroscopic data is millimeter or longer in wavelength and a very limited number of molecules have ever been studied with microwave techniques at wavelengths shorter than 0.3 millimeters. The situation with infrared technique is similarly dire in the submillimeter and far infrared because the black body sources used are competing with a very significant thermal background making the signal to noise poor. Regardless of the technique used the data must be archived in a way useful for the interpretation of observations.

Pearson, J. C.↗
NASA NTRS2004

Hamilton's Equations with Euler Parameters for Rigid Body Dynamics Modeling

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

Shivarama, Ravishankar↗
NASA NTRS1979

Acoustic energy in ducts - Further observations

The transmission of acoustic energy in uniform ducts carrying uniform flow is investigated with the purpose of clarifying two points of interest. The two commonly used definitions of acoustic 'energy' flux are shown to be related by a Legendre transformation of the Lagrangian density exactly as in deriving the Hamiltonian density in mechanics. In the acoustic case the total energy density and the Hamiltonian density are not the same which accounts for two different 'energy' fluxes. When the duct has acoustically absorptive walls neither of the two flux expressions gives correct results. A reevaluation of the basis of derivation of the energy density and energy flux provides forms which yield consistent results for soft walled ducts.

Eversman, W.↗
NASA NTRS2004

Unfolding of Proteins: Thermal and Mechanical Unfolding

We have employed a Hamiltonian model based on a self-consistent Gaussian appoximation to examine the unfolding process of proteins in external - both mechanical and thermal - force elds. The motivation was to investigate the unfolding pathways of proteins by including only the essence of the important interactions of the native-state topology. Furthermore, if such a model can indeed correctly predict the physics of protein unfolding, it can complement more computationally expensive simulations and theoretical work. The self-consistent Gaussian approximation by Micheletti et al. has been incorporated in our model to make the model mathematically tractable by signi cantly reducing the computational cost. All thermodynamic properties and pair contact probabilities are calculated by simply evaluating the values of a series of Incomplete Gamma functions in an iterative manner. We have compared our results to previous molecular dynamics simulation and experimental data for the mechanical unfolding of the giant muscle protein Titin (1TIT). Our model, especially in light of its simplicity and excellent agreement with experiment and simulation, demonstrates the basic physical elements necessary to capture the mechanism of protein unfolding in an external force field.

Hur, Joe S.↗
NASA NTRS1994

Berry phase in Heisenberg representation

We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.

Andreev, V. A.↗