Engineering topics

Eckman, Randy A.

Publications and source records attributed to Eckman, Randy A..

3 records

NASA NTRS2019

Improvements to the Copernicus Trajectory Design and Optimization System for Complex Space Trajectories

The purpose of this assessment was to develop updates and new features for the NASA Copernicus Spacecraft Trajectory Design and Optimization analysis tool (version 5.0) for application to NASA programs and projects. These updates will significantly improve the ability to design and optimize complex trajectories over multiple trajectory phases; will allow the use of unique vehicle-specific guidance, control, and trajectory strategies and constraints; and the creation of an almost unlimited number of unique user-defined capabilities. The primary stakeholders for this assessment are the trajectory design and optimization analysts and engineers, and the chief engineers and project managers for existing programs, projects, and/or tasks that involve impulsive, finite burn, and/or continuous thrust trajectories (e.g., Sun, planet, comet, asteroid, halo orbit, Lagrange point, and distant retrograde orbit). The breadth of application spans the preliminary engineering and mission design concepts and optimization, to the development of candidate reference missions and integrated mission design for vehicle system design and operation, to the design and development of flight trajectories and associated propulsive maneuvers for real-time operations.

Murri, Daniel G.↗

NASA NTRS2016

Normalization and Implementation of Three Gravitational Acceleration Models

Unlike the uniform density spherical shell approximations of Newton, the consequence of spaceflight in the real universe is that gravitational fields are sensitive to the asphericity of their generating central bodies. The gravitational potential of an aspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities that must be removed to generalize the method and solve for any possible orbit, including polar orbits. Samuel Pines, Bill Lear, and Robert Gottlieb developed three unique algorithms to eliminate these singularities. This paper documents the methodical normalization of two of the three known formulations for singularity-free gravitational acceleration (namely, the Lear and Gottlieb algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre polynomials and Associated Legendre Functions (ALFs) for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Eckman, Randy A.↗

NASA NTRS2011

Normalization of Gravitational Acceleration Models

Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Eckman, Randy A.↗