Trajectory generation by piecewise spline interpolation
Abstract
A method of generating vehicle trajectories from sets of position coordinates, acceleration components, or velocity vector directions specified at discrete points in time is described. The method uses piecewise cubic spline polynomials fitted to the trajectory position coordinates, thus ensuring continuity of position, velocity, and acceleration along the trajectory. The mathematical basis of cubic spline interpolation is derived, and the description of a computer program for generating the trajectory interpolating polynomial coefficients is included in the report. Calculation of vehicle Euler angles is also contained as an option in the program; these are expressed as interpolating polynomial coefficients in a manner similar to that used for the trajectory. The Euler angle calculation permits the inclusion of aerodynamic angles of attack for an airsupported vehicle under the assumption that all maneuvers use coordinated turns.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 April 1976
 Bibcode:
 1976STIN...7716093J
 Keywords:

 Missile Trajectories;
 Polynomials;
 Spline Functions;
 Trajectory Control;
 Acceleration (Physics);
 Computerized Simulation;
 Interpolation;
 Position (Location);
 Launch Vehicles and Space Vehicles