astrodynx.equ_of_orb_uvi

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astrodynx.equ_of_orb_uvi#

astrodynx.equ_of_orb_uvi(U0, U1, U2, r0, sigma0)[source]#

The equation of orbit using universal functions

Parameters:

  • U0 (ArrayLike) – The universal function U0.

  • U1 (ArrayLike) – The universal function U1.

  • U2 (ArrayLike) – The universal function U2.

  • r0 (ArrayLike) – The radius at the initial time.

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

Return type:

ArrayLike

Returns:

The radius.

Notes

The function is defined as:

\[ r = r_0 U_0 + \sigma_0 U_1 + U_2 \]
where \(U_0\) is the universal function U0, \(U_1\) is the universal function U1, \(U_2\) is the universal function U2, \(r_0\) is the radius at the initial time, and \(\sigma_0\) is the sigma function at the initial time.

References

Battin, 1999, pp.178.

Examples

A simple example:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> U0 = 1.0
>>> U1 = 1.0
>>> U2 = 1.0
>>> r0 = 1.0
>>> sigma0 = 0.0
>>> adx.equ_of_orb_uvi(U0, U1, U2, r0, sigma0)
2.0

With broadcasting:

>>> U0 = jnp.array([1.0, 2.0])
>>> U1 = jnp.array([1.0, 2.0])
>>> U2 = jnp.array([1.0, 1.0])
>>> r0 = jnp.array([1.0, 1.0])
>>> sigma0 = jnp.array([0.0, 0.0])
>>> adx.equ_of_orb_uvi(U0, U1, U2, r0, sigma0)
Array([2., 3.], dtype=float32)
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