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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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NASA NTRS1973

The effect of finite thrust and heating constraints on the synergetic plane change maneuver for a space shuttle orbiter-class vehicle

Numerical solutions to the optimal three-dimensional glide/thrust atmosphere skip maneuver are obtained using the multiple shooting iteration scheme. A singular thrust arc, induced by the heating constraints, is encountered. The synergetic plane change maneuver is shown to be superior to an extra-atmospheric one for 556-km (300-nm) circular orbit plane changes of more than 5 degrees.

Dickmanns, E. D.↗

NASA NTRS1973

A new technique for calculating reentry base heating

The laminar base flow field of a two-dimensional reentry body has been studied by Telenin's method. The flow domain was divided into strips along the x-axis, and the flow variations were represented by Lagrange interpolation polynomials in the transformed vertical coordinate. The complete Navier-Stokes equations were used in the near wake region, and the boundary layer equations were applied elsewhere. The boundary conditions consisted of the flat plate thermal boundary layer in the forebody region and the near wake profile in the downstream region. The resulting two-point boundary value problem of 33 ordinary differential equations was then solved by the multiple shooting method. The detailed flow field and thermal environment in the base region are presented in the form of temperature contours, Mach number contours, velocity vectors, pressure distributions, and heat transfer coefficients on the base surface. The maximum heating rate was found on the centerline, and the two-dimensional stagnation point flow solution was adquate to estimate the maximum heating rate so long as the local Reynolds number could be obtained.

Meng, J. C. S.↗

NASA NTRS1988

Guidance and control strategies for aerospace vehicles

The optimal control problem arising in coplanar, orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high Earth orbit to low Earth orbit. A performance index is chosen the minimize the fuel consumpltion for the transfer. Simulations are carried out for establishing a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the paper is the application of an efficient multiple shooting method for taming the notorious nonlinear, two-point, boundary value problem resulting from optimization procedure.

Naidu, Desineni S.↗

NASA NTRS1988

Optimal reentry guidance for aeroassisted orbit transfer vehicles

A three-state model is presented for analyzing the problem of optimal changes in heading with minimum energy loss for a hypersonic gliding vehicle. A further model order reduction to a single state model is examined using singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy of the vehicle. A separate boundary-layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary-layer problem, three guidance laws are obtained, each having a feedback form. The guidance laws are evaluated for a hypothetical vehicle, and compared to an optimal solution obtained using a multiple shooting algorithm.

Calise, Anthony J.↗

NASA NTRS1989

Fuel-optimal trajectories of aeroassisted orbital transfer with plane change

The problem of minimization of fuel consumption during the atmospheric portion of an aeroassisted, orbital transfer with plane change is addressed. The complete mission has required three characteristic velocities, a deorbit impulse at high earth orbit (HEO), a boost impulse at the atmospheric exit, and a reorbit impulse at low earth orbit (LEO). A performance index has been formulated as the sum of these three impulses. Application of optimal control principles has led to a nonlinear, two-point, boundary value problem which was solved by using a multiple shooting algorithm. The strategy for the atmospheric portion of the minimum-fuel transfer is to start initially with the maximum positive lift in order to recover from the downward plunge, and then to fly with a gradually decreasing lift such that the vehicle skips out of the atmosphere with a flight path angle near zero degrees.

Naidu, Desineni Subbaramaiah↗

NASA NTRS1988

Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem

The optimal-control problem arising in coplanar orbital transfer using aeroassist technology is addressed. The maneuver involves the transfer from high earth orbit to low earth orbit with minimum fuel consumption. Simulations are carried out to obtain a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the present work is the application of an efficient multiple shooting method for handling the difficult nonlinear two-point boundary value problem resulting from the optimization procedure.

Naidu, D. S.↗

NASA NTRS1989

Fuel-optimal trajectories of aeroassisted orbital transfer with plane change

Naidu, D. S.↗

NASA NTRS1990

Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem

The optimal control problem arising in coplanar orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high to low earth orbit via the atmosphere, with the object of minimizing the total fuel consumption. Simulations are carried out to obtain the fuel-optimal trajectories for flying the spacecraft through the atmosphere. A highlight is the application of an efficient multiple-shooting method for treating the nonlinear two-point boundary value problem resulting from the optimizaion procedure. The strategy for the atmospheric portion of the minimum-fuel transfer is to fly at the maximum lift-to-drag ratio L/D initially in order to recover from the downward plunge, and then to fly at a negative L/D to level off the flight so that the vehicle skips out of the atmosphere with a flight path angle near zero degrees.

Naidu, Desineni Subbaramaiah↗

NASA NTRS1992

Finite element method for optimal guidance of an advanced launch vehicle

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Hodges, Dewey H.↗

NASA NTRS1992

A hybrid approach to near-optimal launch vehicle guidance

This paper evaluates a proposed hybrid analytical/numerical approach to launch-vehicle guidance for ascent to orbit injection. The feedback-guidance approach is based on a piecewise nearly analytic zero-order solution evaluated using a collocation method. The zero-order solution is then improved through a regular perturbation analysis, wherein the neglected dynamics are corrected in the first-order term. For real-time implementation, the guidance approach requires solving a set of small dimension nonlinear algebraic equations and performing quadrature. Assessment of performance and reliability are carried out through closed-loop simulation for a vertically launched 2-stage heavy-lift capacity vehicle to a low earth orbit. The solutions are compared with optimal solutions generated from a multiple shooting code. In the example the guidance approach delivers over 99.9 percent of optimal performance and terminal constraint accuracy.

Leung, Martin S. K.↗

NASA NTRS1993

Variational Trajectory Optimization Tool Set: Technical description and user's manual

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

Bless, Robert R.↗

NASA NTRS2002

Atmospheric Ascent Guidance for Rocket-Powered Launch Vehicles

An advanced ascent guidance algorithm for rocket- powered launch vehicles is developed. This algorithm cyclically solves the calculus-of-variations two-point boundary-value problem starting at vertical rise completion through main engine cutoff. This is different from traditional ascent guidance algorithms which operate in a simple open-loop mode until high dynamic pressure (including the critical max-Q) portion of the trajectory is over, at which time guidance operates under the assumption of negligible aerodynamic acceleration (i.e., vacuum dynamics). The initial costate guess is corrected based on errors in the terminal state constraints and the transversality conditions. Judicious approximations are made to reduce the order and complexity of the state/costate system. Results comparing guided launch vehicle trajectories with POST open-loop trajectories are given verifying the basic formulation of the algorithm. Multiple shooting is shown to be a very effective numerical technique for this application. In particular, just one intermediate shooting point, in addition to the initial shooting point, is sufficient to significantly reduce sensitivity to the guessed initial costates. Simulation results from a high-fidelity trajectory simulation are given for the case of launch to sub-orbital cutoff conditions as well as launch to orbit conditions. An abort to downrange landing site formulation of the algorithm is presented.

Dukeman, Greg A.↗

NASA NTRS2003

Enhancements to an Atmospheric Ascent Guidance Algorithm

Enhancements to an advanced ascent guidance algorithm for rocket-powered launch vehicles are described. A general method has been developed for conveniently and efficiently handling the common case of (asymmetric) launch vehicles with unbalanced thrust and aerodynamic moments. The new part of this development concerns the treatment of endo-atmospheric flight. An alternative method for handing the transversality conditions has been developed that eliminates the need for a priori elimination of the constant multipliers that adjoin the terminal state constraints to the performance index. As a result, new constraints can be formulated and implemented with relative ease. The problem of burn-coast-burn trajectory optimization is treated using a modified multiple shooting technique.

Dukeman, Greg A.↗

NASA NTRS2003

Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

Pai, P. F.↗

NASA NTRS2003

Fully Nonlinear Modeling and Analysis of Precision Membranes

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Pai, P. Frank↗

NASA NTRS2010

Trajectory Optimization: OTIS 4

The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended.

Riehl, John P.↗

NASA NTRS2014

Trajectory Design for the Transiting Exoplanet Survey Satellite

The Transiting Exoplanet Survey Satellite (TESS) is a National Aeronautics and Space Administration (NASA) mission, scheduled to be launched in 2017. TESS will travel in a highly eccentric orbit around Earth, with initial perigee radius near 17 Earth radii (Re) and apogee radius near 59 Re. The orbit period is near 2:1 resonance with the Moon, with apogee nearly 90 degrees out-of-phase with the Moon, in a configuration that has been shown to be operationally stable. TESS will execute phasing loops followed by a lunar flyby, with a final maneuver to achieve 2:1 resonance with the Moon. The goals of a resonant orbit with long-term stability, short eclipses and limited oscillations of perigee present significant challenges to the trajectory design. To rapidly assess launch opportunities, we adapted the Schematics Window Methodology (SWM76) launch window analysis tool to assess the TESS mission constraints. To understand the long-term dynamics of such a resonant orbit in the Earth-Moon system we employed Dynamical Systems Theory in the Circular Restricted 3-Body Problem (CR3BP). For precise trajectory analysis we use a high-fidelity model and multiple shooting in the General Mission Analysis Tool (GMAT) to optimize the maneuver delta-V and meet mission constraints. Finally we describe how the techniques we have developed can be applied to missions with similar requirements. Keywords: resonant orbit, stability, lunar flyby, phasing loops, trajectory optimization

Stationkeepting↗

NASA NTRS2014

Trajectory Design for the Transiting Exoplanet Survey Satellite (TESS)

The Transiting Exoplanet Survey Satellite (TESS) is a National Aeronautics and Space Administration (NASA) mission launching in 2017. TESS will travel in a highly eccentric orbit around Earth, with initial perigee radius near 17 Earth radii (Re) and apogee radius near 59 Re. The orbit period is near 2:1 resonance with the Moon, with apogee nearly 90 degrees out-of-phase with the Moon, in a configuration that has been shown to be operationally stable. TESS will execute phasing loops followed by a lunar flyby, with a final maneuver to achieve 2:1 resonance with the Moon. The goals of a resonant orbit with long-term stability, short eclipses and limited oscillations of perigee present significant challenges to the trajectory design. To rapidly assess launch opportunities, we adapted the SWM76 launch window tool to assess the TESS mission constraints. To understand the long-term dynamics of such a resonant orbit in the Earth-Moon system we employed Dynamical Systems Theory in the Circular Restricted 3-Body Problem (CR3BP). For precise trajectory analysis we use a high-fidelity model and multiple shooting in the General Mission Analysis Tool (GMAT) to optimize the maneuver delta-V and meet mission constraints. Finally we describe how the techniques we have developed can be applied to missions with similar requirements.

Monte Carlo↗