Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “maximum principle”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

Bart, Timothy J.↗
NASA NTRS1972

Optimal cruise trajectories for supersonic airplanes

Equations are derived for maximizing range for specified initial and final values of mass and altitude. Constant-velocity flight is assumed, and normal acceleration is neglected. The problem is solved by using the maximum principle. Optimal trajectories are obtained and uniqueness is demonstrated. Results are obtained for a supersonic airplane. Curves are presented which can be used to obtain the optimal trajectory and maximum range for a range of initial and final mass and altitude. The optimal range is compared to the range obtained by using the standard cruise trajectory profile (consisting of a Bereguet cruise plus maximum- and minimum-thrust connecting segments) and to the range obtained at constant-altitude cruise.

Teren, F.↗
NASA NTRS1976

Optimal reusable-tug and expendable-kickstage trajectories for high-energy planetary missions including correction for nodal precession

Equations are derived by using branched trajectory optimization techniques and the maximum principle to maximize the payload capability of a reusable tug/expendable kickstage vehicle configuration for planetary missions. The two stages and the payload are launched into a low earth orbit by a single space shuttle. The analysis includes correction for precession of the orbit. This correction is done by the tug. The tug propels the payload and the kickstage to an energy beyond earth escape and returns within a specified time to the precessed orbit. After separating from the tug, the kickstage accelerates the payload to the required injection conditions. Planetary injection conditions are specified by the mission energy and a fixed declination and right ascension of the outgoing asymptote. The multipoint boundary value problem resulting from the analysis is solved by a Newton-Raphson iteration technique. Partial derivatives of the boundary conditions are obtained by perturbing the initial conditions one at a time, integrating the trajectory and adjoint equations, and observing the changes in boundary conditions. Maximum payload capability is derived for two typical mission energies. In addition, the variations of several mission and stage parameters are also examined.

Borsody, J.↗
NASA NTRS1968

Optimal control and stability

Relation between optimal control problem and Liapunov functions, and calculus of variations and maximum principle methods of solving synthesis problems

Letov, A. M.↗
NASA NTRS1967

Study of a global search algorithm for optimal control.

Adaptive random search algorithm utilizing boundary cost-function hypersurfaces measurement to implement Pontryagin maximum principle, discussing hybrid computer use, iterative solution and convergence properties

Brocker, D. H.↗