astrodynx.twobody.lagrange_Ft

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astrodynx.twobody.lagrange_Ft#

astrodynx.twobody.lagrange_Ft(U1, r_mag, r0_mag=1, mu=1)[source]#

The Lagrange Ft function

Parameters:

  • U1 (ArrayLike) – The universal function U1.

  • r_mag (ArrayLike) – The radius at the current time.

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

  • mu (ArrayLike) – The gravitational parameter.

Return type:

Array

Returns:

The value of the Lagrange Ft function.

Notes

The Lagrange Ft function is defined as:

\[ F_t = -\frac{\sqrt{\mu}}{r r_0} U_1 \]
where \(U_1\) is the universal function U1, \(r\) is the radius at the current 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
>>> r = 1.0
>>> r0 = 1.0
>>> mu = 1.0
>>> adx.twobody.lagrange_Ft(U1, r, r0, mu)
Array(-1., dtype=float32, weak_type=True)

With broadcasting:

>>> U1 = jnp.array([1.0, 2.0])
>>> r = jnp.array([1.0, 1.0])
>>> r0 = jnp.array([1.0, 1.0])
>>> mu = jnp.array([1.0, 1.0])
>>> adx.twobody.lagrange_Ft(U1, r, r0, mu)
Array([-1., -2.], dtype=float32)
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