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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Modeling Principles Using the Relation Between Lagrange Multipliers and Bond Graphs

Final document is attached. Modeling dynamic systems by bond graphs has become state of the art technology since hundreds of researchers around the world have incorporated the technology in many fields of engineering and science. The legacy of its invertor Prof. Henry Paynter at MIT in 1959 is now a fundamental and practical technique to understand reality by building computer models. This paper addresses a particular aspect of this technology when modeling of mechanical systems require relaxation of constraints by means of Lagrange principles. Lagrange's equations are a useful means of describing and solving systems with kinematic constraints. Lagrange multipliers are variables used in equations to find the extremes of multivariate functions. Here we explore the relation of Lagrange multipliers to solve modeling difficulties of a space vehicle with equations with dependent derivatives. Lagrange multipliers were used in conjunction with bond graphs to simulate a system where joints of kinematic linkages produce dependent derivatives. NASA's Morpheus Project lunar lander was used as a case study. The Morpheus Project is a terrestrial test vehicle designed to fly the terminal descent trajectory of a lunar lander to advance the Autonomous Landing Hazard Avoidance Technology (ALHAT). An objective of this study is to apply the modeling approach herein to capture the dynamic movement of the lander as the propellant is sloshed and consumed. This paper expands further the analysis presented by (Granda, J J. Nguyen, L, Carlson, T, Sahragard-Monfared, G., Fornalski, E., Brocker 2016). Using an automated approach bond graph models of state space equations were generated using the Computer Aided Modeling Program (CAMPG). Integral causality models and derivative causality models were considered in order to find the simpler solution for the mathematical dependencies produced in modeling this vehicle.

Granda, Jose J.↗
NASA NTRS2011

What Did We Think Could Be Learned About Earth From Lagrange Point Observations?

The scientific excitement surrounding the NASA Lagrange point mission Triana, now called DSCOVR, tended to be forgotten in the brouhaha over other aspects of the mission. Yet a small band of scientists in 1998 got very excited about the possibilities offered by the Lagrange-point perspective on our planet. As one of the original co-investigators on the Triana mission, I witnessed that scientific excitement firsthand. I will bring to life the early period, circa 1998 to 2000, and share the reasons that we thought the Lagrange-point perspective on Earth would be scientifically revolutionary.

Wiscombe, Warren↗
NASA NTRS2015

Investigating Trojan Asteroids at the L4/L5 Sun-Earth Lagrange Points

Investigations of Earth's Trojan asteroids will have benefits for science, exploration, and resource utilization. By sending a small spacecraft to the Sun-Earth L4 or L5 Lagrange points to investigate near-Earth objects, Earth's Trojan population can be better understood. This could lead to future missions for larger precursor spacecraft as well as human missions. The presence of objects in the Sun-Earth L4 and L5 Lagrange points has long been suspected, and in 2010 NASA's Wide-field Infrared Survey Explorer (WISE) detected a 300 m object. To investigate these Earth Trojan asteroid objects, it is both essential and feasible to send spacecraft to these regions. By exploring a wide field area, a small spacecraft equipped with an IR camera could hunt for Trojan asteroids and other Earth co-orbiting objects at the L4 or L5 Lagrange points in the near-term. By surveying the region, a zeroth-order approximation of the number of objects could be obtained with some rough constraints on their diameters, which may lead to the identification of potential candidates for further study. This would serve as a precursor for additional future robotic and human exploration targets. Depending on the inclination of these potential objects, they could be used as proving areas for future missions in the sense that the delta-V's to get to these targets are relatively low as compared to other rendezvous missions. They can serve as platforms for extended operations in deep space while interacting with a natural object in microgravity. Theoretically, such low inclination Earth Trojan asteroids exist. By sending a spacecraft to L4 or L5, these likely and potentially accessible targets could be identified.

John, K. K.↗
NASA NTRSDate not supplied

Lagrange-Based Options for Relay Satellites to Eliminate Earth-Mars Communications Outages During Solar Superior Conjunctions

Recent conjunction class Mars human mission plans have generally assumed that there will inevitably be periods of communications outages between Earth and Mars. This has significant cost and risk implications for not only Mars missions, but also precursor missions in the lunar environment. But are there ways to avoid these outages? The potential exists for communications to be interrupted by Solar Superior Conjunctions (SSCs). Depending on the communications system, used, there can be communications outages up to as many as 78 days. The higher bandwidth systems experience the greatest outage. If these communications channels are interrupted due to an SSC, there are of course resulting challenges to mission operations. An outage of a few days to a few weeks could allow minor disturbances to become major concerns or even trigger subsystems failures. An inability to consult with the ground at the wrong time could result in loss of mission, loss of an element, or loss of life. Each planet in the solar system has a set of five Lagrange points associated with it and the Sun. At any given point in time, a planet or either its L4 or L5 point is visible to any other planet in the solar system, regardless of the position of the sun relative to the two. Thus, L4 and L5 have high value as relay systems to prevent communications outages. There are four sets of solar Lagrange points that may be of potential use in this study: Mars-Sun L4 and L5 points, Earth-Sun L4 and L5, Venus-Sun L4 and L5, and Mercury-Sun L4 and L5. A candidate relay satellite system will be identified, with consideration of both new technology developments and existing telecommunications satellites. This system may have implications for not only the Mars human mission architectures, but also Gateway and human lunar surface architectures as these other studies are tasked with paving the way to human Mars missions. If Mars communications outages can be eliminated, then the degree of autonomy necessary in Mars and precursor systems may be reduced.

Relay Satellite↗
NASA NTRS1982

Sensitivity of constrained linear inversions to the selection of the Lagrange multiplier

The influence of the choice of the Lagrange multiplier on constrained linear inversions is explored, with reference made to applications in inferring the columnar aerosol size distributions from spectral aerosol optical depth measurements. A range of the Lagrange multiplier is examined to find all positive solutions for the solution vector, which represents modifying factors to the assumed form of the size distribution. An iterative method is devised to constrain the calculations to consideration of only positive quantities and a requirement that the regression fit to data be consistent with measurement errors. The determination of the variances and covariances is formulated and applied to existing data sets for optical depth. Variances in the solution are found to be large for particle radii when the information content of the data is small.

King, M. D.↗
NASA NTRS1992

Technique to eliminate computational instability in multibody simulations employing the Lagrange multiplier

A programming technique to eliminate computational instability in multibody simulations that use the Lagrange multiplier is presented. The computational instability occurs when the attached bodies drift apart and violate the constraints. The programming technique uses the constraint equation, instead of integration, to determine the coordinates that are not independent. Although the equations of motion are unchanged, a complete derivation of the incorporation of the Lagrange multiplier into the equation of motion for two bodies is presented. A listing of a digital computer program which uses the programming technique to eliminate computational instability is also presented. The computer program simulates a solid rocket booster and parachute connected by a frictionless swivel.

Watts, G.↗
NASA NTRS1990

Structural optimization with constraints from dynamics in Lagrange

Structural optimization problems are mostly solved under constraints from statics, such as stresses, strains, or displacements under static loads. But in the design process, dynamic quantities like eigenfrequencies or accelerations under dynamic loads become more and more important. Therefore, it is obvious that constraints from dynamics must be considered in structural optimization packages. This paper addresses the dynamics branch in MBB-LAGRANGE. It will concentrate on two topics, namely on the different formulations for eigenfrequency constraints and on frequency response constraints. For the latter the necessity of a system reduction is emphasized. The methods implemented in LAGRANGE are presented and examples are given.

Pfeiffer, F.↗
NASA NTRS2001

Interferometric Characterization of the Earth's Atmosphere from Lagrange Point 2

Part of the NASA plans for future Earth Science missions calls for observations using novel vantage points that can produce science products otherwise unobtainable. Observations of the Earth from the Lagrange-2 point, L-2, (1.5 million km behind the Earth on the Earth-Sun line) affords a unique vantage point for atmospheric science. Spectral observation of the Earth's atmosphere using solar occultation techniques in the near infrared (1 to 4 microns) provides one of the most accurate methods of passively sensing attitude profiles of the major species (CO2, O3, O2, CH4, H2O N2O). While traditional polar orbiting occultation measurements can obtain about 14 measurements per day (2 per orbit), solar occultation observations from the Lagrange-2 point will yield hourly profile measurements at all latitudes. The expected spatial resolution is 2 km in altitude, 0.5 degrees in latitude, and 2 degrees in longitude. The result from 24 hours of observations will be a three-dimensional map of atmospheric composition. To accomplish this task from L-2 requires the development of a large moderate spectral resolution instrument whose entrance aperture is about 10 meters. Use of a standard telescope design with a 10-meter circular mirror or a 10-meter strip mirror would be prohibitively expensive and excessively massive. Instead, we are proposing the development of a 10-meter linear interferometer coupled to a Fourier transform imaging spectrometer. The result will be a highly efficient design with sufficient sensitivity, while having both spatial and spectral resolution to produce the desired results. Preliminary calculations show that seven species (CO2, O3, O2, CH4, H2O N2O) have clearly separated spectral features in the I to 4 microns range with sufficient absorption to produce profile information from near the Earth's surface to the middle stratosphere. For CO2 the estimated sensitivity to change is 0.33% or 1 part in 330. This should be sufficient to detect changes that are significant for the carbon cycle studies. Initial instrument design studies are underway to determine the optimum optical design for the interferometer-spectrometer as well as the necessary highly stable mechanical designs. Separate design studies are being conducted for the spacecraft. shuttle launch facility, low-light solar power design, thermal control, and unique navigation requirements to reach and maintain the tight halo orbit about L-2.

Herman, Jay R.↗
NASA NTRS2001

Simulation of formation flight near Lagrange points for the TPF Mission

In this paper, we focus on an orbit near the L***2***. Lagrange point. Our work in the study of the feasibility of formation flight near the Lagrange points indicates that 1) formation flight near L***2*** is dynamically possible for the TPF Mission and 2) linear control around a nonlinear baseline libration orbit near L***2*** is adequate for the TPF Mission.

TPF↗
NASA NTRS2001

Simulation of formation flight near Lagrange Points for the TPF Mission

The formation flight problem near the Lagrange points is of great interest. Recent work in the study of the feasibility of formation flight near the Lagrange points indicates that 1.) Formation flight near L2 is dynamically possible for the TPF Mission; and 2. Linear control around a nonlinear baseline libration orbit near L2 is adequate for the TPF Mission. This paper provides simulations which validate these conclusions.

TPF↗