A general method for the computation of Cartesian coordinates and partial derivatives of the two-body problem
Cartesian coordinates and partial derivatives of two-body problem as double-precision Fortran 4 program for IBM 7094
FORTRAN↗
SEARCH · Search NASA
Results for “Cartesian”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Cartesian formulation of membrane theory.
Cartesian formulation of membrane theory, discussing equations of equilibrium, strain energy, variation formulation and boundary conditions
CARTESIAN COORDINATE↗
Static Aeroelastic Analysis with an Inviscid Cartesian Method
An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.
Aeroelastic↗
E(n)-Equivariant cartesian tensor message passing interatomic potential
Machine learning potential (MLP) has been a popular topic in recent years for its capability to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due to their remarkable accuracy, and a wave of message passing networks based on Cartesian coordinates has emerged. However, the information of the node in these models is usually limited to scalars, and vectors. In this work, we propose High-order Tensor message Passing interatomic Potential (HotPP), an E(n) equivariant message passing neural network that extends the node embedding and message to an arbitrary order tensor. By performing some basic equivariant operations, high order tensors can be coupled very simply and thus the model can make direct predictions of high-order tensors such as dipole moments and polarizabilities without any modifications. The tests in several datasets show that HotPP not only achieves high accuracy in predicting target properties, but also successfully performs tasks such as calculating phonon spectra, infrared spectra, and Raman spectra, demonstrating its potential as a tool for future research.
97 MATHEMATICS AND COMPUTING↗
Cartesian equivariant representations for learning and understanding molecular orbitals
Qualitative and quantitative orbital properties such as bonding/antibonding character, localization, and orbital energies are critical to how chemists understand reactivity, catalysis, and excited-state behavior. Despite this, representations of orbitals in deep learning models have been very underdeveloped relative to representations of molecular geometries and Hamiltonians. Here, we apply state-of-the-art equivariant deep learning architectures to the task of assigning global labels to orbitals, namely energies characterizations, given the molecular coefficients from Hartree–Fock or density functional theory. The architecture we have developed, the Cartesian Equivariant Orbital Network (CEONET), shows how molecular orbital coefficients are readily featurized as equivariant node features common to all graph-based machine-learned potentials. We find that CEONET performs well at predicting difficult quantitative labels such as the orbital energy and orbital entropy. Furthermore, we find that the CEONET representation provides an intuitive latent space for differentiating orbital character for the qualitative assignment of e.g. bonding or antibonding character. In addition to providing a useful representation for further integrating deep learning with electronic structure theory, we expect CEONET to be useful for automatizing and interpreting the results of advanced electronic structure methods such as complete active space self-consistent field theory. In particular, the ability of CEONET to infer multireference character via the orbital entropy paves the way toward the machine-learned selection of active spaces.
chemical reactions↗
Boundary Effects in the Diffusion of New Products on Cartesian Networks
The Role of Boundaries in the Spreading of Solar Peer effects by neighbors play a key role in the spreading of residential solar. Thus, people are more likely to install a solar system on their roof if some of their neighbors have already done so. Because people who live near the municipality boundary have fewer neighbors, does this imply that they are less likely to adopt solar? In “Boundary Effects in the Diffusion of New Products on Cartesian Networks,” Fibich, Levin, and Gillingham analyze this problem analytically using the Bass model on two-dimensional networks and empirically using data on installations of solar systems. They show that boundaries have a significant impact on the adoption of residential units near the municipality boundary. Their effect on the aggregate adoption in the municipality, however, is negligible.
Business & Economics↗
An efficient method for Cartesian transformations
Cartesian coordinate transformations by rigid vector rotations
Flanagan, P. F.↗
Cartesian-coordinate dimensioning for plumbing systems
Nonprogressive dimensioning method specifies Cartesian coordinates for each critical point in detail drawings of precision plumbing and ducting components to avoid tolerance accumulation. Method permits direct fabrication of tubing shapes without necessitating generation of a preproduction tubing mockup.
Buirgy, P. A.↗
Transonic airfoil design using Cartesian coordinates
A numerical technique for designing transonic airfoils having a prescribed pressure distribution (the inverse problem) is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that inverse boundary conditions and Cartesian coordinates are used. The method is a direct-inverse approach that controls trailing-edge closure. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.
Carlson, L. A.↗
A general time element for orbit integration in Cartesian coordinates
Two techniques are discussed for increasing the accuracy of the numerical integration of eccentric orbits in Cartesian coordinates. One involves the use of an independent variable different from time; this increases the efficiency of the numerical integration. The other uses a time element, which reduces the in-track error. A general expression is given of a time element valid for an arbitrary independent variable. It is pointed out that this time element makes it possible to switch the independent variable merely by applying a scaling factor; there is no need to change the differential equations of the motion. Eccentric, true, and elliptic anomalies are used as independent variables in the case of a transfer orbit for a geosynchronous orbit. The elliptic anomaly is shown to perform much better than the other classical anomalies.
Janin, G.↗
Euler calculations for multielement airfoils using Cartesian grids
A finite volume formulation for the Euler equations using Cartesian grids is presented and used to study complex two-dimensional configurations. The formulation extends methods developed for the potential equation to the Euler equations. Results using this approach for single element airfoils are shown to be competitive with and as accurate as other methods that employ mapped grids. Further, it is demonstrated that this method provides a simple and accurate procedure for solving flow problems involving multielement airfoils.
Clarke, D. K.↗
Approximate Cartesian state transition matrix
Based on a Taylor series expansion, an easily-computed approximation to the Cartesian state transition matrix is presented for a general velocity-independent force field. Suitable for the short time intervals encountered in onboard navigation applications of the extended Kalman filter, it provides approximately five decimal digits of accuracy for earth orbiting spacecraft with update intervals of one minute, and better accuracy for shorter intervals.
Markley, F. L.↗
Direct adaptive control of manipulators in Cartesian space
A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.
Seraji, H.↗
Cartesian path control of a two-degree-of-freedom robot manipulator
The problem of cartesian trajectory control of a closed-kinematic chain mechanism robot manipulator with possible space station applications is considered. The study was performed by both computer simulation and experimentation for tracking of three different paths: a straight line, a sinusoid and a circle. Linearization and pole placement methods are employed to design controller gains. Results show that the controllers are robust and there are good agreements between simulation and experimentation. Excellent tracking quality and small overshoots are also evident.
Nguyen, Charles C.↗
Unsteady viscous-inviscid interaction procedures for transonic airfoils using Cartesian grids
A viscous-inviscid interaction procedure for transonic airfoils using an Euler/integral boundary layer formulation and Cartesian grids is presented. The approach is based on a time dependent formulation for both the integral boundary layer equations and the Euler equations. Effects of upstream history on the shear stress are modeled by a time dependent rate equation derived from the turbulent kinetic energy equation. Results are presented for two of the test cases reported by Cook et al. (1979) for the RAE 2822 supercritical airfoil and one of the cases reported by Harris (1981) for the NACA 0012 symmetric airfoil. In general, the results are in good agreement with experiment.
Fenno, Charles C., Jr.↗
An adaptive Cartesian control scheme for manipulators
A adaptive control scheme for direct control of manipulator end-effectors to achieve trajectory tracking in Cartesian space is developed. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for online implementation with high sampling rates.
Seraji, H.↗
Navier-Stokes calculations using Cartesian grids. I - Laminar flows
A finite-volume formulation for the Navier-Stokes equations using Cartesian grids is used to study flows past airfoils. In addition to the solution of the complete equations, solutions for two simplified versions of the governing equations were obtained and compared with those using body-fitted grids. Results are presented for two airfoil sections, NACA 0012 and RAE 2822, for a range of Mach numbers, angles of attack, and Reynolds numbers. It is shown that the results are highly dependent on the smoothness of the surface grid. Without such smoothness, the skin friction and pressure converge to nonuniform distributions. On the other hand, when surface cells with smoothly varying areas are used, the results compared favorably with calculations employing body-fitted grids.
Frymier, Paul D., Jr.↗
Stable boundary conditions for Cartesian grid calculations
The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.
Berger, M. J.↗