Attitude stability of dissipative dual-spin spacecrafts
Spin-axis attitude stability of dissipative dual spin spacecrafts in force-free environment
Guha, A. K.↗
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An experimental investigation of trailing vortices behind a wing with a vortex dissipator
Trailing vortices behind wing tip with vortex dissipator, using wind tunnel flow visualization and flight tests
Chigier, N.↗
Dissipative systems
The abstract theory presented shows how the theory of dissipative systems of ordinary differential equations can be extended to include a wide class of functional and partial differential equations. Since the basic hypotheses are all in terms of boundedness, finding sufficient conditions in terms of Liapunov functions was not difficult. Work is being undertaken to solve some nontrivial examples to illustrate how the theory can applied.
Lasalle, J. P.↗
Mechanical-wave dissipation in the lower corona: Empirical requirements for quiet regions
The relation between dissipation and temperature structure in the lower corona was empirically determined. This relation was then used in conjunction with the observed structure to estimate the damping length for mechanical waves.
Moore, R. L.↗
Dissipation of electric fields in the ionosphere
The heating and movement of the upper atmosphere at ionospheric levels in response to electric currents are discussed. Joule dissipation, generation of winds, and pressure gradients are significant factors in the energetics of the ionospheric electric currents flowing during magnetic storms and also of the Sq current system.
Cole, K. D.↗
Dissipative effects on nonlinear waves in rotating fluids.
Modifications to the existing inviscid theory of long-wave propagation in rotating fluids are studied. A modification to the Korteweg-deVries equation is found to describe weak dissipation in long waves in a swirling fluid. General features of solutions are discussed, and a solution for the damping of solitary waves is presented.
Leibovich, S.↗
Effects of viscosity and constraints on the dispersion and dissipation of waves in large blood vessels. I.
Investigation of the effects of blood viscosity on dissipation as well as dispersion of small waves in arteries and veins by means of a parametric study. A linearized analysis of axisymmetric waves in a cylindrical membrane that contains a viscous fluid indicates that there are two families of waves: a family of slow waves and one of fast waves. The faster waves are shown to be more sensitive to variations in the elastic properties of the medium surrounding the blood vessels and at high values of the frequency parameter alpha. At low values of alpha the effects of viscosity on attenuation are reversed.
Jones, E.↗
Dissipative systems.
A theory is presented that shows how the concept of dissipative systems of ordinary differential equations can be extended to include a broad class of functional and partial differential equations, such as retarded functional differential equations and parabolic partial differential equations. Since the basic hypotheses are all in terms of boundedness, finding sufficient conditions in terms of Liapunov functions would not be too difficult.
Lasalle, J. P.↗
Topological dissipation and the small-scale fields in turbulent gases.
It is shown that a large-scale magnetic field possesses a hydrostatic equilibrium only if the pattern of small-scale variations is uniform along the large-scale field. Thus equilibrium obtains only if the variations in the field consist of simple twisting of the lines, with the twists extending uniformly the full length of the field. Any more complicated topology, such as two or more flux tubes wrapped around each other to form a rope, or braided or knotted flux tubes, is without equilibrium, no matter what fluid pressures are applied along the individual lines of force. The result is rapid dissipation and field-line merging, which quickly reduces the topology to the simple equilibrium form. The effect explains the absence of strong small-scale fields in the solar photosphere and in interstellar space in spite of the vigorous turbulence.
Parker, E. N.↗
Theory of a general class of dissipative processes.
Development of a theory of periodic processes that is of sufficient generality for being applied to systems defined by partial differential equations (distributed parameter systems) and functional differential equations of the retarded and neutral type (hereditary systems), as well as to systems arising in the theory of elasticity. In particular, the attempt is made to develop a meaningful general theory of dissipative periodic systems with a wide range of applications.
Hale, J. K.↗
Balsa wood as an energy dissipator
Studies have been undertaken to determine response of balsa wood in variety of environmental conditions. Response is dependent upon state of balsa wood as well as environment to which it is exposed, but certain combinations of conditions serve to increase significantly energy-dissipating capacity of wood relative to its normal capacity.
Knoell, A. C.↗
Fixed point theorems and dissipative processes
The deficiencies of the theories that characterize the maximal compact invariant set of T as asymptotically stable, and that some iterate of T has a fixed point are discussed. It is shown that this fixed point condition is always satisfied for condensing and local dissipative T. Applications are given to a class of neutral functional differential equations.
Hale, J. K.↗
Spin reorientation of a nonsymmetric body with energy dissipation
Stable rotating semi-rigid bodies were demonstrated analytically, and verified in flights such as Explorer 1 and ATS-5 satellites. The problem arises from the two potential orientations which the final spin vector can take after large angle reorientation from minor to major axis, i.e., along the positive or negative axis of the maximum inertia. Reorientation of a satellite initially spinning about the minor axis using an energy dissipation device may require that the final spin orientation be controlled. Examples of possible applications are the Apogee Motor Assembly with Paired Satellites (AMAPS) configuration, where proper orientation of the thruster is required; and reorientation of ATS-5, where the spin sensitive nature of the despin device (yo-yo mechanism) requires that the final spin vector point is a specified direction.
Cenker, R. J.↗
Space shuttle GN and C equation document no. 23: Energy dissipation rate guidance for approach phase
The approach guidance routine for taking the space shuttle orbiter from the entry phase of approximately 100,000 feet to the start of the final landing maneuver is discussed. The approach guidance system is a closed feedback loop scheme. The vehicle energy is managed by controlling the rate at which energy is dissipated during a straight in approach. The spacecraft performance during each segment of the approach flight is analyzed. Equations of motion are developed to describe the spacecraft guidance and flight path.
Elias, A.↗
Fixed point theorems and dissipative processes.
Operators of the type considered by Hale et al. (1972) are used to show that under certain conditions there is a fixed point in a dissipative map within a Banach space. The conditions required for the existence of this fixed point are discussed in detail. Several fixed point theorems are formulated and proved.
Hale, J. K.↗
The generation and dissipation of solar and galactic magnetic fields.
Turbulent diffusion of magnetic field plays an essential role in the generation of magnetic field in most astrophysical bodies. Review of what can be proved and what can be believed about the turbulent diffusion of magnetic field. Observations indicate the dissipation of magnetic field at rates that can be understood only in terms of turbulent diffusion. Theory shows that a large-scale weak magnetic field diffuses in a turbulent flow in the same way that smoke is mixed throughout the fluid by the turbulence. The small-scale fields (produced from the large-scale field by the turbulence) are limited in their growth by reconnection of field lines at neutral points, so that the turbulent mixing of field and fluid is not halted by them. Altogether, it appears that the mixing of field and fluid in the observed turbulent motions in the sun and in the Galaxy is unavoidable. Turbulent diffusion causes decay of the general solar fields in a decade or so, and of the galactic field in 100 m.y. to 1 b.y. It is concluded that continual dynamo action is implied by the observed existence of the fields.
Parker, E. N.↗
Thermal structure of the Martian atmosphere during the dissipation of the dust storm of 1971
The secular variation of the thermal structure of the Martian atmosphere during the dissipation phase of the 1971 dust storm is examined, using temperatures obtained by the infrared spectroscopy investigation on Mariner 9. For the latitude range -20 to -30, the mean temperature at the 2mb level is found to decrease from approximately 220K in mid-December 1971 to about 190K by June 1972 while for the 0.3mb level a decrease from 203K to 160K is observed. Over the same period, the amplitude of the diurnal temperature wave also decreased. Assuming a simplified radiative heating model, the dust optical depth is found to decrease approximately exponentially with an e-folding time of about 60 days at both the 0.3 and 2mb levels. Stokes-Cunningham settling alone cannot account for this behavior. Sedimentation models which include both gravitational settling and vertical mixing are developed in an effort to explain the time evolution of the dust.
Conrath, B. J.↗
Control of spin ambiguity during reorientation of an energy dissipating body
A quasi-rigid body initially spinning about its minor principal axis and experiencing energy dissipation will enter a tumbling mode and eventually reorient itself such that stable spin about its major principal axis is achieved. However, in this final state the body may be spinning in a positive or negative sense with respect to its major axis and aligned in a positive or negative sense with the inertially fixed angular momentum vector. This ambiguity can be controlled only through an active system. The associated dynamical formulations and simulations of uncontrolled reorientations are presented. Three control schemes are discussed and results offered for specific examples. These schemes include displacement of internal masses, spinning up of internal inertia, and reaction jets, all of which have demonstrated the ability to control spin ambiguity.
Kaplan, M. H.↗