astrodynx.twobody.lagrange_G

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astrodynx.twobody.lagrange_G#

astrodynx.twobody.lagrange_G(U1, U2, sigma0=0, r0_mag=1, mu=1)[source]#

The Lagrange G function

Parameters:

  • U1 (ArrayLike) – The universal function U1.

  • U2 (ArrayLike) – The universal function U2.

  • sigma0 (ArrayLike) – The sigma function at the initial time.

  • r0_mag (ArrayLike) – The radius at the initial time.

  • mu (ArrayLike) – The gravitational parameter.

Return type:

Array

Returns:

The value of the Lagrange G function.

Notes

The Lagrange G function is defined as:

\[ G = \frac{r_0 U_1 + \sigma_0 U_2}{\sqrt{\mu}} \]
where \(U_1\) is the universal function U1, \(U_2\) is the universal function U2, \(\sigma_0\) is the sigma function at the initial time, \(r_0\) is the radius at the initial time, and \(\mu\) is the gravitational parameter.

References

Battin, 1999, pp.179.

Examples

A simple example:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> U1 = 1.0
>>> U2 = 1.0
>>> sigma0 = 0.0
>>> r0 = 1.0
>>> mu = 1.0
>>> adx.twobody.lagrange_G(U1, U2, sigma0, r0, mu)
Array(1., dtype=float32, weak_type=True)

With broadcasting:

>>> U1 = jnp.array([1.0, 2.0])
>>> U2 = jnp.array([1.0, 1.0])
>>> sigma0 = jnp.array([0.0, 0.0])
>>> r0 = jnp.array([1.0, 1.0])
>>> mu = jnp.array([1.0, 1.0])
>>> adx.twobody.lagrange_G(U1, U2, sigma0, r0, mu)
Array([1., 2.], dtype=float32)
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