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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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

An inverse dynamics approach to trajectory optimization and guidance for an aerospace plane

The optimal ascent problem for an aerospace planes is formulated as an optimal inverse dynamic problem. Both minimum-fuel and minimax type of performance indices are considered. Some important features of the optimal trajectory and controls are used to construct a nonlinear feedback midcourse controller, which not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suited for onboard implementation. Robust ascent guidance is obtained by using combination of feedback compensation and onboard generation of control through the inverse dynamics approach. Accurate orbital insertion can be achieved with near-optimal control of the rocket through inverse dynamics even in the presence of disturbances.

Lu, Ping↗
NASA NTRS2020

NASA’s Space Launch System: Launch Capability for Lunar Exploration and Transformative Science

Excitement is building for the first launch of NASA’s Space Launch System (SLS), a unique exploration asset for the agency’s Artemis lunar program as well as for a new generation of science missions. SLS is designed for an array of missions beyond Earth’s orbit. The flexible system, which can be configured for Orion, cargo or Orion with co-manifested payload missions, offers high escape velocities to send more mass to deep space destinations. When configured with an 8.4 m-diameter fairing, SLS offers unmatched payload volume for human exploration and science missions. The initial Block 1 variant will insert at least 26 metric tons (t) to trans-lunar injection (TLI) and the more powerful Block 1B vehicle will launch 34-37 t to TLI using a new-development upper stage. Much of the initial SLS Block 1 vehicle is complete, including the upper stage and payload section, the core stage, engines and the solid rocket boosters. The first mission, Artemis I, launching from modernized and upgraded facilities at Kennedy Space Center (KSC), will be an uncrewed test flight of SLS, Orion and ground processing, with a primary objective of testing Orion’s heat shield at lunar re-entry velocity. Artemis I will have accommodations for 13 6U CubeSat payloads. These CubeSat missions will be deployed along the upper stage disposal trajectory after Orion separates from the vehicle. A rare opportunity for CubeSats to be deployed beyond low Earth orbit (LEO), Artemis I CubeSat missions range from searching for hydrogen and other volatiles on the lunar South Pole to studying the acceleration mechanisms of solar and interplanetary particles from a heliocentric trajectory. With manufacturing of the initial vehicle complete, fabrication and procurement is progressing for the second flight of SLS and Orion, Artemis II. Also an SLS Block 1 and Orion flight launching from KSC, Artemis II will mark the return of American astronauts to deep space with a lunar flyby-free return trajectory mission. With the Artemis III flight, NASA has the goal to land the first woman and the next man on the Moon. Infrastructure beyond SLS will be required for this effort, including elements of the lunar Gateway as well as lunar rovers, landers and additional commercially supplied launch services. SLS, as the only vehicle with the capability to lift 26 t of mass to TLI in its initial Block 1 variant, will remain a key component of this new-era exploration program. Future variants – Block 1B and Block 2 –will lift 34-45 t to TLI. This paper will discuss the status of testing and integration for the Artemis I vehicle, manufacturing progress for the second vehicle and the manifest outlook for primary, co-manifested and secondary payloads in the current deep space exploration environment.

Creech, Stephen D.↗
NASA NTRS1986

Thrust vectoring for single-stage-to-orbit, horizontal takeoff, horizontal landing, space vehicles

The preliminary design of a horizontal takeoff, horizontal landing, single-stage-to-orbit, rocket-powered space vehicle was performed. The purpose was to examine technology requirements for future small payload launch vehicles. The distinguishing aspect of the design was the utilization of thrust vectoring to provide half of the lift at takeoff. The inclusion of a canard was necessary to provide additional lift at takeoff and to balance the moments produced with thrust vectoring. A weights estimation, an aerodynamic assessment, a trajectory analysis, and a gear weight analysis were performed. The takeoff weight of the resulting vehicle was approximately 1.26 million pounds, based on advanced technology structures and subsystems. The vehicle was designed to deliver a 5000-pound payload to a polar orbit.

Cunningham, M. J.↗
DOE OSTI2020

Transcritical diffuse-interface hydrodynamics of propellants in high-pressure combustors of chemical propulsion systems

Rocket engines and high-power new generations of gas-turbine jet engines and diesel engines oftentimes involve the injection of one or more reactants at subcritical temperatures into combustor environments at high pressures, and more particularly at pressures higher than those corresponding to the critical points of the individual components of the mixture, which typically range from 13 to 50 bars for most propellants. This class of trajectories in the thermodynamic space has been traditionally referred to as transcritical. However, the fundamental understanding of fuel atomization, vaporization, mixing, and combustion processes at such high pressures remains elusive. In particular, whereas fuel sprays are relatively well characterized at normal pressures, analyses of dispersion of fuel in high-pressure combustors are hindered by the limited experimental diagnostics and theoretical formulations available. The description of the thermodynamics of hydrocarbon-fueled mixtures employed in chemical propulsion systems is complex and involves mixing-induced phenomena, including an elevation of the critical point whereby the coexistence region of the mixture extends up to pressures much larger than the critical pressures of the individual components. As a result, interfaces subject to surface-tension forces may persist in multicomponent systems despite the high pressures, and may give rise to unexpected spray-like atomization dynamics that are otherwise absent in monocomponent systems above their critical point. In this article, the current understanding of this phenomenon is reviewed within the context of propulsion systems fueled by heavy hydrocarbons. Emphasis is made on analytical descriptions at mesoscopic scales of interest for computational fluid dynamics. In particular, a set of modifications of the constitutive laws in the Navier–Stokes equations for multicomponent flows, supplemented with a high-pressure equation of state and appropriate redefinitions of the thermodynamic potentials, are introduced in this work based on an extended version of the diffuse-interface theory of van der Waals. The resulting formulation involves revisited forms of the stress tensor and transport fluxes of heat and species, and enables a description of the mesoscopic volumetric effects induced by transcritical interfaces consistently with the thermodynamic phase diagram of the mixture at high pressures. Additionally, applications of the theory are illustrated in canonical problems, including dodecane/nitrogen transcritical interfaces in non-isothermal systems. The results indicate that a transcritical interface is formed between the propellant streams that persists downstream of the injection orifice over distances of the same order as the characteristic thermal-entrance length of the fuel stream. The transcritical interface vanishes at an edge that gives rise to a fully supercritical mixing layer.

02 PETROLEUM↗
NASA NTRS1999

A Co-Investigator Project for the Cornell University Cleft Accelerated Plasma Experimental Rocket-CAPER

The CAPER rocket campaign was to follow the SCIFER experiment as a detailed study of the ion acceleration processes in the Cleft Ion Fountain (CIF) above 1000 km altitude. The SCIFER rocket demonstrated that the experiment was feasible and that the CIF acceleration processes on the dayside are different from those observed in the discrete aurora on the nightside. The responsibility of the GI/UAF co-investigator project was to provide the real-time acquisition and display of large-and small-scale ground observations, and satellite solar wind data at the launch control center at Longyearbyen, Svalbard for the determination of the launch conditions and the later interpretation of the rocket observations. The rocket campaign was proposed for January of 1998, but was slipped to January of 1999. The rocket was launched on January 21, 1999 at 06 h 13 m 30 s UT. All of the GI/UAF co-investigator systems functioned well, except the narrow-field TV camera which was to follow the 140 km conjugate of the payload on command from GPS tracking data sent from Andoya. The data were not available during the flight, and the camera tracked the nominal conjugate. Unfortunately, the trajectory was well west of nominal, so no useful narrow-field conjugate data were acquired . In addition, the payload missed the region of more intense precipitation, brighter aurora, stronger currents, and likely large fluxes of transverse ion acceleration. On the other hand, good data were acquired across a region of the ionosphere that appears to have had a double convection boundary because of the IMF switching its z component shortly before launch. These data are important for understanding the reaction of the magnetosphere and ionosphere to changes in the IMF.

Deehr, Charles S.↗
NASA NTRS2000

A Flight Demonstration of Plasma Rocket Propulsion

The Advanced Space Propulsion Laboratory at the NASA Johnson Space Center has been engaged in the development of a variable specific impulse magnetoplasma rocket (V ASIMR) for several years. This type of rocket could be used in the future to propel interplanetary spacecraft and has the potential to open the entire solar system to human exploration. One feature of this propulsion technology is the ability to vary its specific impulse so that it can be operated in a mode that maximizes propellant efficiency or a mode that maximizes thrust. Variation of specific impulse and thrust enhances the ability to optimize interplanetary trajectories and results in shorter trip times and lower propellant requirements than with a fixed specific impulse. In its ultimate application for interplanetary travel, the VASIMR would be a multi-megawatt device. A much lower power system is being designed for demonstration in the 2004 timeframe. This first space demonstration would employ a lO-kilowatt thruster aboard a solar powered spacecraft in Earth orbit. The 1O-kilowatt V ASIMR demonstration unit would operate for a period of several months with hydrogen or deuterium propellant with a specific impulse of 10,000 seconds.

Petro, Andrew↗
NASA NTRSDate not supplied

Post-Flight Performance Analysis of Navigation and Advanced Guidance Algorithms on a Terrestrial Suborbital Rocket Flight

There is currently renewed interest in robotic and crewed landers for a return to the lunar surface. Advanced guidance and navigation algorithms are essential to accurately delivering cargo and crew safely to the moon successfully. This paper reports the overall performance of an integrated set of navigation and guidance algorithms flown on a terrestrial suborbital rocket up to an altitude of approximately 100km. The navigation algorithm consists of an onboard extended Kalman Filter (EKF) that ingests multiple sensor measurements, one of which is the output from a terrain relative navigation (TRN) algorithm that cross-references camera images to on-board satellite imagery to perform feature correlation within the camera image. The guidance algorithm solves for a 6-degree-of-freedom (DoF) optimal trajectory using a successive convexification method during powered descent. The altitude range as well as the landing dynamics experienced during this test flight are realistic for an extraterrestrial landing and provide an invaluable data set to gauge the current development of these landing algorithms in an effort to advance the overall software readiness levels (SRL). This paper will delve into different aspects of each algorithm and present an analysis of the in-flight performance of the algorithms. This flight was conducted under the National Aeronautics and Space Administration (NASA) Safe and Precise Landing Integrated Capabilities Evolution (SPLICE) project focused on technology advancement for landing applications.

Guidance↗
NASA NTRS1973

Preliminary guided rocket feasibility study.

The feasibility of actively guiding sounding rockets to reduce impact dispersion has been investigated. The theoretical probability of Range Safety thrust termination for several high performance rockets was combined with the cost of acquiring the extended range at White Sands Missile Range (WSMR) to establish a guidance system price ceiling of $20K per flight. Guiding the Black Brant VC for the first five seconds of flight results in sufficient dispersion reduction to impact within the standard range boundaries at WSMR. The guidance system thrust level required to statically control the vehicle to a nominal-wind weighted trajectory for five seconds is between 150-200 pounds. A six-degree-of-freedom trajectory program with guidance simulation capability has been developed and the equations are delineated in this paper.

Nolan, M. B.↗
NASA NTRS1993

A Generalized Eulerian-Lagrangian Analysis, with Application to Liquid Flows with Vapor Bubbles

Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined Eulerian-Lagrangian technique, in which Eulerian conservation equations are solved for the liquid phase, while Lagrangian equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the Lagrangian analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.

Dejong, Frederik J.↗
NASA NTRS2019

Guidance, Navigation, and Control for NASA Lunar Pallet Lander

The NASA Lander Technology project is leading the development and integration of the Lunar Pallet Lander (LPL) concept. The objective is to demonstrate precision landing by delivering a payload to the lunar surface within 100 meters of a landing target. Potential landing sites are selected near the lunar pole where water may be present in permanently shadowed regions that could enable future in-situ resource utilization. The LPL is part of a sequence of missions aimed at maturing the necessary technologies, such as lunar precision landing sensors, that will enable the next generation of multi-ton lunar payloads and human landers. This paper provides an overview of the Mission Design, Guidance Navigation and Control (GNC) algorithms, and sensor suite. The results show the LPL simulated trajectory and landing precision performance under nominal and dispersed conditions. The landing precision simulation confirms the need to rely on high-accuracy navigation techniques and sensors such as Terrain Relative Navigation (TRN) and the Navigation Doppler Lidar (NDL), currently being developed for space applications. The results also demonstrate the ability of the guidance and control system to perform a soft lunar touchdown by combining thrust vector control during the solid rocket motor deceleration phase, and pulse engine control, for the liquid powered descent phase.

Orphee, Juan↗
NASA NTRS1973

Preliminary guided rocket feasibility study

The feasibility of actively guiding sounding rockets to reduce impact dispersion has been investigated. The theoretical probability of range safety thrust termination for several high performance rockets was combined with the cost of acquiring the extended range at White Sands Missile Range (WSMR) to establish a guidance system price ceiling of $20K per flight. Guiding the Black Brant VC (BBVC) for the first five seconds of flight results in sufficient dispersion reduction to impact within the standard range boundaries at WSMR. The guidance system thrust level required to statically control the vehicle to a nominal-wind weighted trajectory for five seconds is between 150-200 pounds. A six-degree-of-freedom trajectory program with guidance simulation capability has been developed and the equations are presented.

Nolan, M. B.↗
NASA NTRS2010

Ares I First Stage Propulsion System Status

With the retirement of the Space Shuttle inevitable, the US is faced with the need to loft a reliable cost-effective, technologically viable solution to bring the nation s fleet of spacecraft back up to industry standard. It must not only support the International Space Station (ISS), it must also be capable of supporting human exploration beyond low Earth orbit (LEO). NASA created the Constellation Program to develop a new fleet including the launch vehicles, the spacecraft, and the mission architecture to meet those objectives. The Ares First Stage Team is tasked with developing a propulsion system capable of safely, dependably and repeatedly lofting that new fleet. To minimize technical risks and development costs, the Solid Rocket Boosters (SRBs) of Shuttle were used as a starting point in the design and production of a new first stage element. While the first stage will provide the foundation, the structural backbone, power, and control for launch, the new propulsive element will also provide a greater total impulse to loft a safer, more powerful, fleet of space flight vehicles. Substantial design and system upgrades were required to meet the mass and trajectory requisites of the new fleet. Noteworthy innovations and design features include new forward structures, new propellant grain geometry, a new internal insulation system, and a state-of-the art avionics system. Additional advances were in materials and composite structures development, case bond liners, and thermal protection systems. Significant progress has been made in the design, development and testing of the propulsion and avionics systems for the new first stage element. Challenges, such as those anticipated with thrust oscillation, have been better characterized, and are being effectively mitigated. The test firing of the first development motor (DM-1) was a success that validated much of the engineering development to date. Substantive data has been collected and analyzed, allowing the Ares First Stage team to move forward, fine-tune the design, and advance to production of the second development motor (DM-2), which is now in fabrication. This paper will provide an overview of the design, development, challenges, and progress on the production of the new Ares First Stage propulsion system

Priskos, Alex S.↗
NASA NTRS1985

Filament wound data base development, revision 1

The objective was to update the present Space Shuttle Solid Rocket Booster (SRB) baseline reentry aerodynamic data base and to develop a new reentry data base for the filament wound case SRB along with individual protuberance increments. Lockheed's procedures for performing these tasks are discussed. Free fall of the SRBs after separation from the Space Shuttle Launch Vehicle is completely uncontrolled. However, the SRBs must decelerate to a velocity and attitude that is suitable for parachute deployment. To determine the SRB reentry trajectory parameters, including the rate of deceleration and attitude history during free-fall, engineers at Marshall Space Flight Center are using a six-degree-of-freedom computer program to predict dynamic behavior. Static stability aerodynamic coefficients are part of the information required for input into this computer program. Lockheed analyzed the existing reentry aerodynamic data tape (Data Tape 5) for the current steel case SRB. This analysis resulted in the development of Data Tape 7.

Sharp, R. Scott↗
NASA NTRS2000

Mission Design Overview for Mars 2003/2005 Sample Return Mission

In May 2003, a new and exciting chapter in Mars exploration will begin with the launch of the first of three spacecraft that will collectively contribute toward the goal of delivering samples from the Red Planet to Earth. This mission is called Mars Sample Return (MSR) and will utilize both the 2003 and 2005 launch opportunities with an expected sample return in October 2008. NASA and CNES are major partners in this mission. The baseline mission mode selected for MSR is Mars orbit rendezvous (MOR), analogous in concept to the lunar orbit rendezvous (LOR) mode used for Apollo in the 1960s. Specifically, MSR will employ two NASA-provided landers of nearly identical design and one CNES-provided orbiter carrying a NASA payload of rendezvous sensors, orbital capture mechanisms, and an Earth entry vehicle (EEV). The high-level concept is that the landers will launch surface samples into Mars orbit, and the orbiter will retrieve the samples in orbit and then carry them back to Earth. The first element to depart for Mars will be one of the two landers. Currently, it is proposed that an intermediate class launch vehicle, such as the Boeing Delta 3 or Lockheed Martin Atlas 3A, will launch this 1800-kg lander from Cape Canaveral during the May 2003 opportunity. The lander will utilize a Type-1 transfer trajectory with an arrival at Mars in mid-December 2003. Landing will be aided by precision approach navigation and a guided hypersonic entry to achieve a touchdown accuracy of 10 km or better. Although the exact landing site has not yet been determined, it is estimated that lander resource constraints will limit the site to between 15 degrees north and south latitudes. Following touchdown, the lander will deploy a six-wheeled, 60-kg rover carrying an extensive suite of instruments designed to aid in the analysis of the local terrain and collection of core samples from selected rocks. The surface mission is currently designed around a concept called the surface traverse. Each traverse will involve the rover exploring a selected area of terrain up to 100 meters from the lander, the collection of rock core samples, and the delivery of the samples from the traverse back to a sample canister on the lander. Planning estimates indicate that up to three traverses may be possible during the expected 90-sol lifetime of the lander. The canister that will receive the samples from the rover will be attached to the top stage of a small solid-fueled rocket mounted to the deck of the lander. This rocket is called the Mars Ascent Vehicle (MAV) and consists of three stages weighing a total of about 140 kg. After the conclusion of the surface mission, the MAV will lift-off and insert the sample canister into a near-circular orbit with an altitude of about 600 km and inclination of 45 degrees. The sample canister will wait in this orbit until it is retrieved by the orbiter sometime in early 2007. In August 2005, the second lander and a CNES-provided orbiter weighing 2700 kg will depart for Mars. Currently, it is proposed that a single Ariane 5 provided by CNES will launch both of these two elements onto a Type-2 transfer trajectory. Although the orbiter and lander will be launched together, they will separate shortly after injection and will fly to Mars as two independent spacecraft. However, both spacecraft will perform a maneuver between 10 and 15 days after launch so that their arrival times at Mars differ by between 12 and 24 hours. This scheme will reduce the operational complexity at the encounter date. A set of four 60-kg surface probes will ride piggyback on the orbiter to Mars. These CNES-provided probes are called Netlanders and will serve as surface stations for scientific investigations independent of the Mars Sample Return goals. Starting approximately one month prior to arrival at Mars, the orbiter will begin to release the Netlanders one at a time. Each release cycle will take several days, and will include time for precision navigation to execute one or two maneuvers that will target the Netlanders to their proper landing site. All four deployment cycles will be completed prior to 10 days before arrival. Both the orbiter and lander will arrive in late-July 2006. Upon arrival, the lander will perform a precision landing and surface mission similar in concept to the one that was executed during the 2003 opportunity. Although the landing site for the 2005 opportunity has not been selected, it is expected to be different from the 2003 site to enhance the diversity of the collected samples. The orbiter's arrival at Mars will be highlighted by the first use of aerocapture to insert a spacecraft into a capture orbit around another planet. The choice of aerocapture, as opposed to a propulsive orbit insertion, was considered mission enabling due to a reduction of over 2000 m/s in mission AV. Aerocapture will be targeted to produce a 250 km x 1400 km capture orbit with an inclination of 45 degrees. Current analysis indicates that achieving this goal will require approximately six minutes of flight deep in the atmosphere with a targeted periapsis of approach of about 43 km. After factoring into account the penalty for carrying a heat shield to survive aerocapture, the net savings compared to a propulsive orbital insertion amounts to several hundred kilograms.

Lee, Wayne J.↗
NASA NTRS1988

Apollo Lightcraft Project

This second year of the NASA/USRA-sponsored Advanced Aeronautical Design effort focused on systems integration and analysis of the Apollo Lightcraft. This beam-powered, single-stage-to-orbit vehicle is envisioned as the shuttlecraft of the 21st century. The five person vehicle was inspired largely by the Apollo Command Module, then reconfigured to include a new front seat with dual cockpit controls for the pilot and co-pilot, while still retaining the 3-abreast crew accommodations in the rear seat. The gross liftoff mass is 5550 kg, of which 500 kg is the payload and 300 kg is the LH2 propellant. The round trip cost to orbit is projected to be three orders of magnitude lower than the current space shuttle orbiter. The advanced laser-driven 5-speed combined-cycle engine has shiftpoints at Mach 1, 5, 11 and 25+. The Apollo Lightcraft can climb into low Earth orbit in three minutes, or fly to any spot on the globe in less than 45 minutes. Detailed investigations of the Apollo Lightcraft Project this second year further evolved the propulsion system design, while focusing on the following areas: (1) man/machine interface; (2) flight control systems; (3) power beaming system architecture; (4) re-entry aerodynamics; (5) shroud structural dynamics; and (6) optimal trajectory analysis. The principal new findings are documented. Advanced design efforts for the next academic year (1988/1989) will center on a one meter+ diameter spacecraft: the Lightcraft Technology Demonstrator (LTD). Detailed engineering design and analyses, as well as critical proof-of-concept experiments, will be carried out on this small, near-term machine. As presently conceived, the LTD could be constructed using state of the art components derived from existing liquid chemical rocket engine technology, advanced composite materials, and high power laser optics.

Myrabo, Leik N.↗
NASA NTRS1993

Trajectory optimization based on differential inclusion

A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a 1-D rocket ascent problem ('Goddard Problem') in presence of a dynamic pressure constraint.

Seywald, Hans↗
NASA NTRS1993

Trajectory optimization based on differential inclusion

A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a 1-D rocket ascent problem (`Goddard Problem') in presence of a dynamic pressure constraint.

Seywald, Hans↗
NASA NTRS1993

Trajectory optimization based on differential inclusion

A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a I-D rocket ascent problem ('Goddard Problem') in presence of a dynamic pressure constraint.

Seywald, Hans↗