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Numerical Solution to Vinti’s Problem
- Source :
- Journal of Guidance, Control, and Dynamics. 38:1757-1764
- Publication Year :
- 2015
- Publisher :
- American Institute of Aeronautics and Astronautics (AIAA), 2015.
-
Abstract
- A practical, calculable solution to Vinti’s problem is offered. Vinti’s problem describes the motion of a satellite orbiting an oblate planet, including the point mass and oblateness J2 terms and differing from the actual geopotential only at the higher harmonics. Vinti’s original solution is extended to cover motion over a rotating Earth. An eccentric-anomaly-like transform removes the singularities in the elliptic integrals, rendering them accessible to numerical calculation. The prediction problem requires the simultaneous solution of two “Kepler’s equations.” Reduction to canonical action angle variables can also be accomplished via numerical techniques. This new realization of Vinti’s solution is free of series expansions that limit accuracy and uses only simple well-understood numerical techniques. Possible use of Vinti’s solution for further efforts is discussed.
- Subjects :
- Geopotential
Point particle
Eccentric anomaly
Applied Mathematics
Aerospace Engineering
Kepler's equation
Action-angle coordinates
symbols.namesake
Classical mechanics
Space and Planetary Science
Control and Systems Engineering
symbols
Applied mathematics
Elliptic integral
Astrophysics::Earth and Planetary Astrophysics
Electrical and Electronic Engineering
Series expansion
Newton's method
Mathematics
Subjects
Details
- ISSN :
- 15333884 and 07315090
- Volume :
- 38
- Database :
- OpenAIRE
- Journal :
- Journal of Guidance, Control, and Dynamics
- Accession number :
- edsair.doi...........6d4ba4d60a7dbc8ebec635d6cd057e1e