OPTIMUM TRAJECTORIES
Abstract
The calculus of variations was used to determine (1) What path should a missile with a fixed period of thrust fly to maximize its range at a specified final velocity and altitude, (2) What path should an aircraft fly after take-off to minimize its time of flight to level-flight, combat velocity at a specified altitude. The resulting equations are computationally difficult to handle because of their complexity and quasi-stable nature. Moreover, the new variables introduced by the calculus of variations have no apparent physical meaning, which makes the analysis of their influence difficult. This paper outlines the experiences obtained in solving calculus of variations problems on the REAC. A modified form of the equations (presented as an appendix to this paper) was developed which not only was more satisfactory computationally, but also showed that the calculus of variations equations described the motion of a body similar to the one under study. The nature of the REAC solutions suggested that the steady-state, or mid-path, trajectory and the transient trajectories from the steady-state path to the endpoints could be computed separately. The results using this method agreed well with the exact solution and gave a tremendous savings in computing time.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 15, 1951
- Accession Number
- AD0422812
Entities
People
- Arnold S. Mengel
Organizations
- RAND Corporation