astrodynx.twobody.sigma_fn

Contents

astrodynx.twobody.sigma_fn#

astrodynx.twobody.sigma_fn(pos_vec, vel_vec, mu=1)[source]#

The sigma function

Parameters:

  • pos_vec (ArrayLike) – (…,3) The position vector.

  • vel_vec (ArrayLike) – (…,3) The velocity vector.

  • mu (ArrayLike) – The gravitational parameter.

Return type:

Array

Returns:

The value of the sigma function.

Notes

The sigma function is defined as:

\[ \sigma = \frac{\boldsymbol{r} \cdot \boldsymbol{v}}{\sqrt{\mu}} \]
where \(\boldsymbol{r}\) is the position vector, \(\boldsymbol{v}\) is the velocity vector, and \(\mu\) is the gravitational parameter.

References

Battin, 1999, pp.174.

Examples

A simple example of calculating the sigma function with a position vector of [1, 0, 0], a velocity vector of [0, 1, 0], and a gravitational parameter of 1.0:

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> pos_vec = jnp.array([1.0, 0.0, 0.0])
>>> vel_vec = jnp.array([0.0, 1.0, 0.0])
>>> mu = 1.0
>>> adx.twobody.sigma_fn(pos_vec, vel_vec, mu)
Array([0.], dtype=float32)

With broadcasting, you can calculate the sigma function for multiple position and velocity vectors:

>>> pos_vec = jnp.array([[1.0, 0.0, 0.0], [2.0, 0.0, 0.0]])
>>> vel_vec = jnp.array([[0.0, 1.0, 0.0], [0.0, 2.0, 0.0]])
>>> mu = jnp.array([[1.0], [2.0]])
>>> adx.twobody.sigma_fn(pos_vec, vel_vec, mu)
Array([[0.],
       [0.]], dtype=float32)
Contents