2. First integrals

The two-body problem admits several first integrals, in particular those of angular momentum, energy and eccentricity vector.

A prime integral of a dynamic system is a quantity that remains constant over time. Knowledge of prime integrals enables us to delimit the possible evolutions of a system, even when no analytical solution exists.

2.1 Kinetic moment

The angular momentum per unit mass is $\vec{h} = \vec{r} \land \vec{v}$ where

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Bibliography

(1) - BATTIN (R.) - An introduction to the mathematics and methods of astrodynamics. - AIAA (1999).
(2) - CAPDEROU (M.) - Satellites : de Kepler au GPS. - Springer (2012).
(3)...

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