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The concept of dissipative Hamiltonian system is converted to Lorentz-covariant form, with evolution generated jointly by two scalar functionals, the Lagrangian action and the global entropy. A bracket formulation yields the local covariant laws of energy-momentum conservation and of entropy production. The formalism is illustrated by a derivation of the covariant Landau kinetic equation.
A numerical integration was employed to show that the 3/1 Kirkwood gap region between Jupiter and the sun can serve as the source for asteroidal debris that strikes the earth as chondrites. A previous study by Wetherill (1968) considered planetary close encounters, secular resonances, collisional destruction in space and subsequent atmospheric abrasion of the chondrites. The factors would have resulted in chaotic trajectories for asteroids in the asteroid belt, i.e., eccentricities large enough to make the objects earth-crossing. A sampling of trajectories which could reach large eccentricities is integrated in terms of deterministic solutions of Hamiltonian systems of equations which behave erratically and are dependent on the initial conditions. The examinations successfully predicted a trajectory with a peak eccentricity of 0.652, a time interval of 340,000 yr, and a semimajor axis between 2.4-2.53 AU that was earth-crossing.
Differential equations that arise in astrodynamics are examined from the standpoint of Lie group theory. A summary of the Lie method is given for first degree differential equations. The Kepler problem in Hamiltonian form is treated by this method. Extension of the Lie method to optimal trajectories is outlined.
The GeH radical has been detected in its ground 2 Pi state in the gas phase reaction of fluorine atoms with GeH4 by laser magnetic resonance techniques. Rotational transitions within both 2 Pi 1/2 and 2 Pi 3/2 manifolds have been observed at far-infrared wavelengths and rotational transitions between the two fine structure components have been detected at infrared wavelengths (10 microns). Signals have been observed for all five naturally occurring isotopes of germanium. Nuclear hyperfine structure for H-1 and Ge-73 has also been observed. The data for the dominant isotope (/Ge-74/H) have been fitted to within experimental error by an effective Hamiltonian to give a set of molecular parameters for the X 2 Pi state which is very nearly complete. In addition, the dipole moment of GeH in its ground state has been estimated from the relative intensities of electric and magnetic dipole transitions in the 10 micron spectrum to be 1.24(+ or - 0.10) D.
The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.
Hybrid codes in which part of the plasma is represented as particles and the rest as a fluid are discussed. In the past few years such codes with particle ions and massless, fluid electrons have been applied to space plasmas, especially to collisionless shocks. All of these simulation codes are one-dimensional and similar in structure, except for how the field equations are solved. The various approaches that are used (resistive Ohm's law, predictor-corrector, Hamiltonian) are described in detail and results from the various codes are compared with examples taken from collisionless shocks and low frequency wave phenomena upstream of shocks.
It is found that the effective Hamiltonian for nuclear rotation in a diatom is equivalent to that of a charged particle in a background magnetic-monopole field. In certain cases, half-integer orbital angular momentum or non-Abelian fields occur. Furthermore, the effects of magnetic-monopole-like gauge fields can be experimentally observed in spin-resonance experiments with variable magnetic fields.
Relativistic corrections to the Bethe sum rule have been obtained for a one-electron system. The relativistic sum is first derived assuming completeness by employing the Dirac Hamiltonian. Then, a semirelativistic approach to order v-squared/c-squared is presented following the Foldy-Wouthuysen transformation scheme to exclude the contributions from the negative-energy states. The results have wide applications in high-Z systems at large momentum transfers.
Far-infrared laser magnetic resonance (LMR) spectroscopy was used to calculate the frequencies, wavelengths, and line strengths for transitions of O-(18)H molecules at microwave and far-infrared frequencies. In this experiment, a molecular transition frequency is tuned into coincidence with that of a fixed frequency laser by the application of a variable magnetic field. The O-(18)H radicals, detected in natural abundance (0.20 percent), were produced by the reaction of hydrogen atoms with nitrogen dioxide. These data together with microwave frequencies ascertained by Gottlieb, Redford, and Smith (1974) were used to determine the parameters of an effective Hamiltonian. Rotational levels up to J = 5.5 were involved. Results are indicated schematically and the low-lying energy levels of O-(18)H are shown. It is concluded that the frequencies of transitions between levels studied directly in the LMR experiment are reliable.
A general relationship is established between wave-packet evolution and quantization in classically integrable systems. Because of wave-packet spreading, one cannot simply take the Fourier transform of the time evolution of a wave-packet. Instead, one must propagate the wave-packet using the actions as Hamiltonians. The energy eigenvalues which result are the Einstein-Brillouin-Keller values, and new forms for the eigenfunctions appear. These are free of caustic singularities, and represent averages of wave packets over the invariant torus.
Results are reported of several simulations of the motions of small objects in two-dimensional cellular flows performed to study the evolution of the distributions of particle flows over time in processes such as sedimentation. Stream functions are defined in the form of a Hamiltonian system for the particle motions, with inertial and particle acceleration being neglected. Conditions are found for which the particles will become trapped in an oscillatory motion or the particle orbits attain an oscillary motion. Various simulation images are provided to illustrate the usefulness of the technique for modeling fractal swarms.
To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.
The problems of large-angle attitude maneuvers of a spacecraft have gained much consideration in recent years. The configurations of the spacecraft considered are: completely rigid, a combination of rigid and flexible parts, or gyrostat-type systems. The performance indices usually include minimum torque integration, power criterion, and frequency-shaped cost functionals. The minimum time slewing problem of a rigid spacecraft was examined. Optimal control theory (Maximum Principal) was applied to the slewing motion of a general rigid spacecraft. Control torque about all three axes was computed. The equations for the system are composed of the Euler dynamical equations in the spacecraft body axes and the quaternion kinematical equation. By introducing the costates for the quaternion and the angular velocity, the Hamiltonian of the system can be formed and the optimal control obtained. Finally the methods are applied to the SCOLE slewing motion. The control variables include three control moments on the Shuttle and two control forces on the reflector. Numerical results are discussed.
Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.
The new linear molecule reported by Cernicharo et al. (1986) has been found in the same laboratory discharge in which C3H is observed, establishing conclusively that the molecule is C5H in its 2Pi ground state. Six rotational transitions in the 2Pi(1/2) ladder and four in the 2Pi(3/2), each split by lambda doubling, were observed. The twenty millimeter-wave lines were simultaneously fit by a standard Hamiltonian with five free parameters: the fine-structure constant, the rotational constant, the centrifugal distortion constant, and two lambda-doubling constants.
A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced. These variables simplify the constraints of general relativity considerably and enable one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory. The imbedding suggests new ways of attacking a number of problems in both classical and quantum gravity. Some illustrative applications are discussed.
The excitation energies and oscillator strengths are calculated for electric-dipole-allowed and intercombination transitions between 3s2 1S, 3s3p(1,3)P0, 3p2 3P, 1D, 1S and 3s3d(1,3)D states in Ar VII, Ca IX, and Fe XV ions of the magnesium sequence. These states are represented by the fairly large configuration-interaction expansions. The calculations have been carried out in both LS and intermediate coupling schemes. The relativistic corrections have been included through the Breit-Pauli Hamiltonian. The results are compared with previous theoretical calculations and with measurements.
A new optically detected magnetic resonance spectrum in Al(x)Ga(1-x)As is reported and assigned to native Ga interstitials. Luminescence-quenching signals were observed over the energy region from 0.75 to 1.1 eV. The optically detected magnetic resonance is nearly isotropic, with spin-Hamiltonian parameters g = 2.025 + or - 0.006, central hyperfine splitting A(Ga-69) = 0.050 + or - 0.001/cm, and A(Ga-71) = 0.064 + or - 0.001/cm for H near the 001 line. The strong hyperfine coupling denotes an electronic state of A1 symmetry, which current theories predict for the Ga interstitial but not the Ga antisite. The slight anisotropy probably indicates that the Ga(i) is paired with a second, unknown defect.