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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Effect of the mass center shift for force-free flexible spacecraft

For a spinning flexible spacecraft the mass center generally shifts relative to the nominal undeformed position. It is thought that this shift of center complicates spacecraft stability analysis. It is proved, on the basis of results achieved by Meirovitch and Calico (1972), that for the general class of force-free single-spin flexible spacecraft it is possible to ignore this shift of center without affecting the stability criteria in any significant way. A new theorem on inequalities for quadratic forms is proved to demonstrate the validity of the stability analysis.

Meirovitch, L.↗
NASA NTRS1993

Cenozoic crustal rotations in the Mojave Desert from paleomagnetic studies around Barstow, California

Paleomagnetic data from the Mojave Desert around Barstow, California, suggest 55 to 75 deg of clockwise rotation of this area in earliest Miocene time, followed by 23 deg of counterclockwise rotation in the Early Miocene, and no rotation after 18 Ma. Earliest Miocene clockwise rotation of the Barstow area is suggested by data from nine sites in the Oligocene-Miocene Lane Mountain Quartz Latite and Jackhammer Formation and may be related to oroclinal bending of the southern Sierra Nevada batholith. Data from 13 sites in the Early Miocene Pickhandle Formation indicate counterclockwise rotation, which coincides with Early Miocene E-NE - W-SW extension and detachment faulting in the Mojave Desert. These results suggest that Miocene extension in the Mojave Desert is related to similarly oriented extension in the Colorado River extensional corridor. Early Miocene to Pliocene rocks of the Andesite and Dacite of the Calico Mountains, Barstow Formation, Andesite of Murphy's Well, and Black Mountain Basalt show no evidence for significant rotation of the Barstow area after 18 Ma. Most other paleomagnetic data from elsewhere in the Mojave are consistent with a lack of significant post-18 Ma rotations, suggesting that post-10 Ma right-lateral faulting there has produced relatively little crustal rotation.

Valentine, Michael J.↗
NASA NTRS2004

Control of Initialized Fractional-Order Systems

Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order compensators. Finally the compensator concept is generalized by the use of a continuum of fractions in the compensator via the concept of order-distributions. The last section introduces fractional feedback in discrete-time.

Hartley, Tom T.↗
NASA NTRS1972

The stability of motion of satellites with flexible appendages

The mathematical formulation associated with the problem of stability of motion of a satellite consisting of a main rigid body and three (or less) pairs of flexible rods is presented. The rods are capable of flexure in two orthogonal directions. Whereas the rotational motion of the body is described by generalized coordinates depending on time alone, the elastic displacements of the rods depend both on spatial position and time. Assuming no external torques, there exist motion integrals in the form of momentum integrals. These integrals can be regarded as constraint equations relating the system velocities, and used to reduce the number of variables describing the motion. The stability analysis has been carried out by means of an extension of the Liapunov direct method. Since the elastic vibrations result in energy dissipation, it is shown that the equilibrium position is asymptotically stable if the Hamiltonian is positive definite and unstable if it can take negative values in the neighborhood of the equilibrium. Determining the sign definiteness of the Hamiltonian is complicated by the fact that it contains spatial derivatives of the elastic displacements. Two methods are presented to cope with this problem. The first, the standard modal analysis in conjunction with series truncation, develops criteria in terms of infinite series associated with the natural modes and frequencies of the elastic rods. The second, the method of integral coordinates, yields closed-form stability criteria involving the system parameters, such as the body moments of inertia, the length and mass distribution of the rods, the lowest natural frequencies of the rods, and the satellite spin velocity.

Meirovitch, L.↗
NASA NTRS1972

A comparative study of stability methods for flexible satellites.

This paper compares three approaches to the stability of hybrid dynamical systems, all three methods being based on the Liapunov direct method. The first method uses testing density functions, whereas the second involves defining certain integral coordinates. Both the method using testing density functions and the method of integral coordinates lead to closed-form stability criteria in terms of the system parameters. Criteria obtained using the method of integral coordinates are in general less restrictive than those derived by the method using testing density functions. On the other hand, the latter method is easier to apply and requires less work than the former. The third method is the standard modal analysis. The modal analysis generally yields more involved criteria, depending on the number of modes used to represent the elastic displacements. As an application, the attitude stability of an earth-pointing satellite with multi-elastic domains is investigated.

Meirovitch, L.↗
NASA NTRS1988

Angle of attack estimation using an inertial reference platform

This paper presents the mathematical development and flight test results of an angle of attack estimation system based on inertial navigation system inputs. The estimator uses these inputs to determine the coefficient of lift required at any instant inflight. Angle of attack is then modeled through a regression analysis based on coefficient of lift, altitude and Mach. Overall correlation of the estimator as tested was generally within 0.5 degrees through 17 degrees angle of attack on an F-15A aircraft. A robustness analysis indicates that the system can be used adequately in maneuvering flight.

Zeis, Joseph E., Jr.↗