Date of Award
2013
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mechanical Engineering
Committee Chair
Jason Cassibry
Committee Member
Jonathan Rogers
Committee Member
Nathan Slegers
Committee Member
David Landrum
Committee Member
Robert A. Frederick
Subject(s)
Hypersonic aerodynamics, Astrodynamics, Space trajectories, Applied mechanics
Abstract
An equation of motion has been derived that may be solved using simple analytic functions which describes the motion of a projectile launched from the surface of the Earth into space accounting for both Newtonian gravity and aerodynamic drag. The equation of motion is based upon the Kepler equation of motion differential and variable transformations with the inclusion of a decaying angular momentum driving function and appropriate simplifying assumptions. The new equation of motion is first compared to various numerical and analytical trajectory approximations in a non-rotating Earth reference frame. The Modified Kepler solution is then corrected to include Earth rotation and compared to a rotating Earth simulation. Finally, the modified equation of motion is used to predict the apogee and trajectory of projectiles launched into space by the High Altitude Research Project from 1961 to 1967. The new equation of motion allows for the rapid equalization of projectile trajectories and intercept solutions that may be used to calculate firing solutions to enable ground launched projectiles to intercept or rendezvous with targets in low Earth orbit such as ballistic missiles.
Recommended Citation
Stutz, John David, "Analytical evaluation of the trajectories of hypersonic projectiles launched into space" (2013). Dissertations. 29.
https://louis.uah.edu/uah-dissertations/29