Two-Body Orbital Boundary Value Problems in Regularized Coordinates
| Autor: | Bharat Mahajan, Srinivas R. Vadali |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
020301 aerospace & aeronautics
Polynomial Basis (linear algebra) Transcendental equation Mathematical analysis Aerospace Engineering 02 engineering and technology 01 natural sciences Lambert's problem Transfer orbit 0203 mechanical engineering Space and Planetary Science 0103 physical sciences Boundary value problem Orbit (control theory) 010303 astronomy & astrophysics Trajectory (fluid mechanics) Mathematics |
| Zdroj: | The Journal of the Astronautical Sciences. 67:387-426 |
| ISSN: | 2195-0571 0021-9142 |
| DOI: | 10.1007/s40295-019-00204-0 |
| Popis: | Lambert’s two-body orbital boundary value problem (BVP) is the determination of the terminal velocity vectors of a trajectory connecting two fixed positions in a specified transfer time. The solution to Lambert’s problem is often the basis for preliminary trajectory design and optimization. In this work, several related two-body orbital BVPs, with constraints involving terminal velocities, flight-path angle, Δv, final radius, transfer angle, etc., are studied. Exact solutions to these BVPs are derived in a universal form via the Kustaanheimo-Stiefel transformation. The solutions are regular and completely analytic if the energy of the transfer orbit is known a priori. Otherwise, they require root-finding of either a polynomial or a transcendental equation with well-defined bounds on its roots. The algorithms developed are validated on several orbit transfer problems and can enable complex mission analysis and parametric studies or serve as initial guesses for high-fidelity numerical optimization schemes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink