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Results for “partial derivative”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

King, H. F.↗
NASA NTRS2014

Partial Derivatives of the Lambert Problem

A procedure for deriving analytic partial derivatives of the Lambert problem is presented. Using the universal, cosine based Lambert formulation; first order partial derivatives of the velocities with respect to the positions and times are developed. Taking advantage of inherent symmetries and intermediate variables, the derivatives are expressed in a computationally efficient form. The added cost of computing these partials is found to be approximately 10% to approximately 60% of the Lambert compute cost. The availability of analytic partial derivatives increases optimization speed, efficiency and allows for trajectory optimization formulations that implicitly enforce continuity constraints via embedded Lambert problems.

trajectory computation↗
DOE OSTI2017

Adjoint-based constant-mass partial derivatives

In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, k eff of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2023

Implementing a VLBI Time Delay Model for Earth-orbiting Satellites: Partial derivatives and Verification

This document describes the partial derivatives for commonly estimated parameters including antenna positions, satellite position, and satellite velocity from a near-field VLBI delay model for Earth-orbiting satellites. This model was presented in the Journal of Geodesy by Jaron & Nothnagel (2019). In this context, we present a streamlined version of the near-field VLBI delay. From this simplified model, we deduce a delay rate expression and calculate partial derivatives, maintaining only the terms with significant impact on the computed derivatives’ magnitude. To verify the accuracy of the simplified model and the partial derivatives computed from it, we have created a simple simulation in Matlab of an Earth-orbiting satellite at the altitude of a typical Global Navigation Satellite Systems (GNSS) satellite. From this simulation, we compare the simplified and original delays, and we verify the magnitude and direction of the partial derivatives against the numerically computed derivatives from the original delay model. The partial derivatives and simplified VLBI delay model detailed here are implemented in Fortran in the open-source library VTD.

Geodesy↗
NASA NTRS1972

Analytic partial derivatives for estimating low-thrust parameters.

Analytic partial derivatives for estimating orbital low-thrust parameters via differential correction are developed and compared with two different numerical methods. The formulation is independent of the particular thrust model used and is applicable to all physically possible elliptic orbits. The starting point for the development is the set of variational equations of the elliptic orbital elements in the form due to Lagrange. The first time derivatives of the elements are transformed to derivatives with respect to the space variable, true anomaly, and integrated to first order in closed form in a straightforward general perturbations approach, with one exception: particular attention is given to the mean anomaly as influenced by thrust perturbations in the semimajor axis so that the complete first-order effect is included. The partials of the elements are then taken with respect to any given thrust parameter. Two comparisons are made with numerical methods for computing these thrust partials: numerical quotients and numerical integration of the variational equations for thrust.

Cunningham, G. W.↗
NASA NTRSDate not supplied

Analytical Partial Derivatives of the Q-Law Guidance Algorithm

One method of producing low-thrust trajectories is the closed-loop Q-Law guidance algorithm. This work wraps Q-Law inside a nonlinear programming problem to search for locally optimal gain combinations and enforce nonlinear constraints on the initial state. Gradient-based trajectory optimization has been shown to benefit greatly when analytical partial derivatives are supplied to the optimizer. This paper presents the Q-Law optimization problem setup and derives the Q-Law thrust vector partial derivatives for the State Transition Matrix required by standard nonlinear optimization software.

Jackson L Shannon↗
NASA NTRS2006

AIRS CO2 Retrievals Using the Method of Vanishing Partial Derivatives (VPD)

This document consists of presentation slides that review the work being done with observations from the Atmospheric Infrared Sounder (AIRS) using the concept of Vanishing Partial Derivatives. The infrared region is where several minor gases such as CO2, O3, CO, CH4 and SO2 are radiatively active.

Atmospheric Infrared Sounder (AIRS)↗