Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

Details Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

Apr 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cemda.103..327m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 103, Issue 4, pp.327-342

Astronomy and Astrophysics

Astronomy

1

Planar Motion, Dynamical Equations Of Atmospheric Re-Entry, Analytical Solutions For Differential Equations, Exponential Integral, Generalized Exponential Integral

Scientific paper

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.

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