Numerical solutions for lunar orbits

Massimiliano Vasile, Amalia E. Finzi

Research output: Contribution to conferencePaper

Abstract

Starting from a variational formulation based on Hamilton’s Principle, the paper exploits the finite element technique in the time domain in order to solve orbital dynamic problems characterised by constrained boundary value rather than initial value problems. The solution is obtained assembling a suitable number of finite elements inside the time interval of interest, imposing the desired constraints, and solving the resultant set of non-linear algebraic equations by means of Newton-Raphson method. In particular, in this work this general solution strategy is applied to periodic orbits determination. The effectiveness of the approach in finding periodic orbits in the unhomogeneous gravity field of the Moon is assessed by means of relevant examples, and the results are compared with those obtained by standard time marching techniques as well as with analytical results.
LanguageEnglish
PagesPaper IAF-97-A.5.08
Publication statusPublished - 6 Oct 1997
Event48th International Astronautical Congress - Turin, Italy
Duration: 6 Oct 199710 Oct 1997

Conference

Conference48th International Astronautical Congress
CountryItaly
CityTurin
Period6/10/9710/10/97

Fingerprint

Orbits
Initial value problems
Moon
Newton-Raphson method
Nonlinear equations
Gravitation

Keywords

  • Hamilton's Principle
  • finite element modelling techniques
  • periodic orbits determination

Cite this

Vasile, M., & Finzi, A. E. (1997). Numerical solutions for lunar orbits. Paper IAF-97-A.5.08. Paper presented at 48th International Astronautical Congress, Turin, Italy.
Vasile, Massimiliano ; Finzi, Amalia E. / Numerical solutions for lunar orbits. Paper presented at 48th International Astronautical Congress, Turin, Italy.
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Vasile, M & Finzi, AE 1997, 'Numerical solutions for lunar orbits' Paper presented at 48th International Astronautical Congress, Turin, Italy, 6/10/97 - 10/10/97, pp. Paper IAF-97-A.5.08.

Numerical solutions for lunar orbits. / Vasile, Massimiliano; Finzi, Amalia E.

1997. Paper IAF-97-A.5.08 Paper presented at 48th International Astronautical Congress, Turin, Italy.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Numerical solutions for lunar orbits

AU - Vasile, Massimiliano

AU - Finzi, Amalia E.

PY - 1997/10/6

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N2 - Starting from a variational formulation based on Hamilton’s Principle, the paper exploits the finite element technique in the time domain in order to solve orbital dynamic problems characterised by constrained boundary value rather than initial value problems. The solution is obtained assembling a suitable number of finite elements inside the time interval of interest, imposing the desired constraints, and solving the resultant set of non-linear algebraic equations by means of Newton-Raphson method. In particular, in this work this general solution strategy is applied to periodic orbits determination. The effectiveness of the approach in finding periodic orbits in the unhomogeneous gravity field of the Moon is assessed by means of relevant examples, and the results are compared with those obtained by standard time marching techniques as well as with analytical results.

AB - Starting from a variational formulation based on Hamilton’s Principle, the paper exploits the finite element technique in the time domain in order to solve orbital dynamic problems characterised by constrained boundary value rather than initial value problems. The solution is obtained assembling a suitable number of finite elements inside the time interval of interest, imposing the desired constraints, and solving the resultant set of non-linear algebraic equations by means of Newton-Raphson method. In particular, in this work this general solution strategy is applied to periodic orbits determination. The effectiveness of the approach in finding periodic orbits in the unhomogeneous gravity field of the Moon is assessed by means of relevant examples, and the results are compared with those obtained by standard time marching techniques as well as with analytical results.

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Vasile M, Finzi AE. Numerical solutions for lunar orbits. 1997. Paper presented at 48th International Astronautical Congress, Turin, Italy.