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Results for “LaSalle”

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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14 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1966

Liapunov's second method.

Liapunov second method and stability theory of autonomous and certain nonautonomous systems

LIAPUNOV FUNCTION↗
NASA NTRS1966

Liapunov's second method

Stability theorem based on Liapunov function, and using invariance property of limit sets of solutions to differential equations

THEOREM PROVING↗
NASA NTRS1971

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.↗
NASA NTRS1971

Generalized invariance principles and the theory of stability.

Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.

Lasalle, J. P.↗
NASA NTRS1972

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.↗
NASA NTRS1972

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.↗
NASA NTRS1973

Stark broadening of high-principal-quantum-number n-alpha lines of hydrogen.

High n-alpha lines (transitions n + 1 to n) with quantum numbers n between 50 and 250 have been observed emanating from galactic H II regions where the electron density and temperature are about 1000/cu cm and 1 eV, respectively. High n-alpha lines have not previously been seen in the laboratory where fairly homogeneous plasmas may be produced and relatively precise measurements of electron densities and temperatures can be made. The present work describes experiments where the first members of the hydrogen line series with lower states n = 10, 11, 12, and 13 have been detected in a laboratory plasma. The width of the 12-alpha line at 88.7 microns could be measured and was consistent with calculated broadening from elastic electron collisions and quasi-static ion effects.

Lasalle, T. R.↗