astrodynx.angular_momentum

astrodynx.angular_momentum(pos_vec, vel_vec)

Returns the specific angular momentum of a two-body system.

Parameters:

• pos_vec (ArrayLike) – (…, 3) position vector of the object in the two-body system.

• vel_vec (ArrayLike) – (…, 3) velocity vector of the object in the two-body system, which shape broadcast-compatible with pos_vec.

Return type:

Array

Returns:

The specific angular momentum vector of the object in the two-body system.

Notes

The specific angular momentum is calculated using the cross product of the position and velocity vectors:

\[ \boldsymbol{h} = \boldsymbol{r} \times \boldsymbol{v} \]

where \(\boldsymbol{h}\) is the specific angular momentum, \(\boldsymbol{r}\) is the position vector, and \(\boldsymbol{v}\) is the velocity vector.

References

Battin, 1999, pp.115.

Examples

A simple example of calculating the specific angular momentum for a position vector [1, 0, 0] and velocity vector [0, 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])
>>> adx.angular_momentum(pos_vec, vel_vec)
Array([0., 0., 1.], dtype=float32)

With broadcasting, you can calculate the specific angular momentum 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]])
>>> adx.angular_momentum(pos_vec, vel_vec)
Array([[0., 0., 1.],
       [0., 0., 4.]], dtype=float32)