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 where
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First integrals
Keplerian movement
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