astrodynx.utils.rotmat3dy

astrodynx.utils.rotmat3dy(angle)

Returns a 3x3 rotation matrix for a given angle around the y-axis.

Parameters:

angle (ArrayLike) – The angle in radians to rotate around the y-axis.

Return type:

Array

Returns:

A 3x3 rotation matrix that rotates vectors around the y-axis by the specified angle.

Notes

The rotation matrix is defined as:

\[\begin{split} R_y(\theta) = \begin{bmatrix} \cos(\theta) & 0 & \sin(\theta) \\ 0 & 1 & 0 \\ -\sin(\theta) & 0 & \cos(\theta) \end{bmatrix} \end{split}\]

where \(\theta\) is the angle of rotation.

References

Battin, 1999, pp.85.

Examples

Creating a rotation matrix for a 90-degree rotation (π/2 radians):

>>> import jax.numpy as jnp
>>> import astrodynx as adx
>>> angle = jnp.pi / 2
>>> jnp.allclose(adx.utils.rotmat3dy(angle), jnp.array([[0., 0., 1.], [0., 1., 0.], [-1., 0., 0.]]), atol=1e-7)
Array(True, dtype=bool)

Broadcasting with an array of angles:

>>> angles = jnp.array([0.0, jnp.pi / 2])
>>> results = jnp.stack([adx.utils.rotmat3dy(a) for a in angles])
>>> expected0 = jnp.eye(3)
>>> expected1 = jnp.array([[0., 0., 1.], [0., 1., 0.], [-1., 0., 0.]])
>>> jnp.allclose(results[0], expected0, atol=1e-7)
Array(True, dtype=bool)
>>> jnp.allclose(results[1], expected1, atol=1e-7)
Array(True, dtype=bool)