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Results for “Calculus of variations and optimization”

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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1965

On stochastic extremum problems - calculus.

Lagrange multiplier technique for determining stationary points /of functions/ or stationary functions /of integrals/ of expected value of random functions with certain random constraints

LAGRANGE MULTIPLIER↗
NASA NTRS1976

Optimum solar-sail interplanetary trajectories

A description is given of the optimization of solar-sail interplanetary trajectories. The optimization procedure is based on the calculus of variations. Attention is given to aspects of thrust optimization, optimization criteria, a terrestrial planet rendezvous, the Venus and Mars rendezvous, the Mercury rendezvous, and an asteroid roundtrip mission. The investigation shows that a solar-sail spacecraft represents a viable option for the exploration of the solar system in the future.

Sauer, C. G., Jr.↗
NASA NTRS1973

Effects of inclination and eccentricity on optimal trajectories between earth and Venus

The true optimal transfers, including the effects of the inclination and eccentricity of the planets' orbits, between earth and Venus are presented as functions of the corresponding idealized Hohmann transfers. The method of determining the optimal transfers using the calculus of variations is presented. For every possible Hohmann window, specified as a continuous function of the longitude of perihelion of the Hohmann trajectory, the corresponding numerically exact optimal two-impulse transfers are given in graphical form. The cases for which the optimal two-impulse transfer is the absolute optimal, and those for which a three-impulse transfer provides the absolute optimal transfer are indicated. This information furnishes everything necessary for quick and accurate orbit calculations for preliminary Venus mission analysis. This makes it possible to use the actual optimal transfers for advanced planning in place of the standard Hohmann transfers.

Gravier, J.-P.↗
NASA NTRS1991

SeGRAm - A practical and versatile tool for spacecraft trajectory optimization

An implementation of the Sequential Gradient/Restoration Algorithm, SeGRAm, is presented along with selected examples. This spacecraft trajectory optimization and simulation program uses variational calculus to solve problems of spacecraft flying under the influence of one or more gravitational bodies. It produces a series of feasible solutions to problems involving a wide range of vehicles, environments and optimization functions, until an optimal solution is found. The examples included highlight the various capabilities of the program and emphasize in particular its versatility over a wide spectrum of applications from ascent to interplanetary trajectories.

Rishikof, Brian H.↗
NASA NTRS2019

Investigation of Direct Force Control for Planetary Aerocapture at Neptune

In this work, a direct force control numerical predictor-corrector guidance architecture is developed to enable Neptune aerocapture using flight-heritage blunt body aeroshells. A linear aerodynamics model is formulated for a Mars Science Laboratory-derived aeroshell. The application of calculus of variations shows that the optimal angle of attack and side-slip angle control laws are bang-bang. A closed-loop numerical predictor-corrector direct force control guidance algorithm is developed and numerically simulated using the Program to Optimize Simulated Trajectories II. The Monte Carlo simulated trajectories are demonstrated to be robust to the modeled dispersions in aerodynamics, atmospheric density, and entry state. An aerocapture technology trade study demonstrates that blunt body direct force control aerocapture enables similar performance as slender body bank angle control but halves the peak g-loading.

Deshmukh, Rohan G.↗
DOE OSTI2025

Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

Applied Dynamical Systems↗