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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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Stabilization of unstable two-point boundary value problems, noting field method for avoiding computer storage problems during integration of related differential equations
Approximate solution of two-point boundary value problem
Modified quasilinearization concept for solving nonlinear two point boundary value problem
Nonlinear two-point boundary-value problem solution by combined techniques of quasilinearization and method of particular solutions
Particular solutions for linear two-point boundary value problems with regard to digital computers
Newton-Raphson method generalized for solution of two-point boundary value problems of nonlinear optimal control theory for digital solution
Spacecraft guidance - boundary value problem
Offset vector iteration method for two point boundary value problems, discussing parameters selection, convergence and computation flow diagram
Method of particular solutions used to solve two point boundary value problem for nonlinear controlled system
Particular solutions in nonlinear two point boundary value problems, showing convergence for uncontrolled and controlled systems
Lighthill generalized functions applied to solving two-point boundary value problems in optimal control theory
Low thrust trajectory optimization, using Newton- Raphson method to solve nonlinear two-point boundary value problem
Low thrust trajectory optimization, using Newton- Raphson method to solve nonlinear two-point boundary value problem
Quasi-optimum control technique based on Hamiltonian to solve two-point boundary value problem for nonlinear system
Generalized indirect method solving two-point boundary value problems for rapid optimal trajectory computation
A technique is described in which the two-point boundary value problem (TPBVP) may be solved with the aid of interactive computer graphics. The particular TPBVP considered is the optimal electric propulsion space trajectory problem. An appropriate two-dimensional projection of the TPBVP mapping, or trajectory, is displayed on the computer's television screen, and a man-in-the-loop varies selected trajectory starting conditions in the fashion of a nonlinear walk until the viewed trajectory endpoint lies near a displayed target. Once global targeting is accomplished in this manner, program internal logic can easily handle local targeting to strongly solve the TPBVP.
Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 less than or equal to Pe less than or equal to 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 less than or equal to Da less than or equal to 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r, Theta) = Sum of c(n)(r)P(n)(cos Theta) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions Pn(cos Theta), the variable coefficient PDE can be reduced to a system of N + 1 second order ODEs for the radial functions c(sub n)(r), n = 0, 1, 2,..., N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N + 1) first order differential equations as a two-point boundary value problem on 1 less than or equal to r less than or equal to r(sub infinity). Convergence of the expansion for a specific value of N can thus be established and provides 'spectral' behavior as well as the full concentration field c(r, Theta).
A trajectory-optimization process is described in which the optimum thrust equations are derived using the calculus of variations. The magnitude of the thrust is constrained within an upper and a lower bound, but the thrust direction is arbitrary. This formulation allows both the constant-thrust program and the variable-thrust program to be considered. For the constant-thrust program, certain propulsion-system parameters are optimized for maximum final vehicle mass. This theory has been used to study interplanetary missions to Venus and Mars using a power-limited propulsion system. Both one-way and round trip rendezvous trajectories are considered. The analysis employs a two-body inverse-square force-field model of three dimensions. An iterative routine used to solve the two-point boundary-value problem is described in the Appendix.