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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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Shear deformation and rotary inertia effects on modal data of nonuniform beam, with complex behavior defined by ordinary differential equations
Controllability of distributed-parameter control systems is mathematically studied. A general theory for control systems includes those that cannot be described by ordinary differential equations.
Seven studies have been conducted on research in the existence and nature of solutions of the restricted problems of three and four bodies. The details and results of five of these research investigations have already been published, and the latest two studies will be published shortly. A complete bibliography of publications is included in this report. This research has been primarily qualitative and has yielded new information on the behavior of trajectories near the libration points in the Earth-Moon-Sun and Sun-Jupiter-Saturn systems, and on the existence of periodic trajectories about the libration points of the circular and elliptical restricted four-body models. We have also implemented Birkhoff's normalization process for conservative and nonconservative Hamiltonian systems with equilibrium points. This makes available a technique for analyzing stability properties of certain nonlinear dynamical systems, and we have applied this technique to the circular and elliptical restricted three-body models. A related study was also conducted to determine the feasibility of using cislunar periodic trajectories for various space missions. Preliminary results suggest that this concept is attractive for space flight safety operations in cislunar space. Results of this research will be of interest to mathematicians, particularly those working in ordinary differential equations, dynamical systems and celestial mechanics; to astronomers; and to space guidance and mission analysts.
Transformation of control problems to ordinary differential equations
Necessary and sufficient conditions for optimal strategies for differential /two person zero-sum/ game with sum determined by ordinary differential equations
Stability and error bounds in numerical integration of ordinary differential equations, determining highest possible degree of stable finite difference form
Quasi-linear ordinary differential equations solutions for steady two dimensional stagnation point flows of nonNewtonian power law fluids
Two variable expansion method applied to ordinary differential equation and two wave propagation problems, comparing results with matched asymptotic expansions and coordinate stretching methods
Fifth-order pseudo-Runge-Kutta methods for numerical solution of ordinary differential equations, determining optimal parameters
Integrator design to provide subroutines for numerical solution of ordinary differential equations
Green function in solving linear and nonlinear second order ordinary differential equations including examples in finding rendezvous and periodic orbits of restricted three body system
Linear ordinary differential equation systems first order output sensitivity coefficients generation and application to second order cross sensitivities
Generalized relaxation methods application to transonic flow problems, combining with numerical integration theory for ordinary differential equations
Development of algorithm provides automatic computation of quadratic estimate of domain of stability for stable equilibrium states of nonlinear systems of ordinary differential equations.
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.
A method is presented for obtaining numerical solutions to a certain class of two-point boundary value problems which arise in optimal control theory. The problems are characterized by systems of nonlinear ordinary differential equations with nonlinear boundary conditions.
Axisymmetric responses are presented of a nonshallow thin-walled spherical shell on the basis of nonlinear bending theory. An ordinary differential equation with nonlinearity of quadratic as well as cubic terms associated with variable time is derived. The derivation is based on the assumption that the deflection mode is the sum of four Legendre polynomials, and the Galerkin procedure is applied. The equation is solved by asymptotic expansion, and a first approximate solution is adopted. Unstable regions of this solution are discussed.
An extension of classical methods of optimal control theory for systems described by ordinary differential equations to distributed-parameter systems described by partial differential equations is presented. An application is given involving the minimum-mass design of a simply-supported shear plate with a fixed fundamental frequency of vibration. An optimal plate thickness distribution in analytical form is found. The case of a minimum-mass design of an elastic sandwich plate whose fundamental frequency of free vibration is fixed. Under the most general conditions, the optimization problem reduces to the solution of two simultaneous partial differential equations involving the optimal thickness distribution and the modal displacement. One equation is the uniform energy distribution expression which was found by Ashley and McIntosh for the optimal design of one-dimensional structures with frequency constraints, and by Prager and Taylor for various design criteria in one and two dimensions. The second equation requires dynamic equilibrium at the preassigned vibration frequency.