Attitude Representations¶

The astrojax.attitude_representations module provides four interconvertible 3D rotation representations, elementary rotation functions, and pure conversion kernels. All types use JAX primitives and are compatible with jax.jit, jax.vmap, and jax.grad.

Representation Types¶

Type	Internal Storage	Degrees of Freedom	Page
`Quaternion`	`[w, x, y, z]` shape `(4,)`	4 (unit constraint)	Quaternion
`RotationMatrix`	shape `(3, 3)`	9 (SO(3) constraint)	Rotation Matrix
`EulerAngle`	`(order, phi, theta, psi)`	3 angles + order	Euler Angles
`EulerAxis`	`(axis(3,), angle)`	3 axis + 1 angle	Euler Axis

Additional Components¶

Component	Description	Page
Elementary Rotations	`Rx`, `Ry`, `Rz` axis-aligned rotation matrix constructors	Elementary Rotations
Conversions	Pure conversion kernels operating on raw JAX arrays	Conversions

Conversion Graph¶

All four types provide to_* instance methods and from_* class methods for full interconvertibility. Most conversions route through the quaternion representation internally:

from astrojax import Quaternion, RotationMatrix, EulerAngle, EulerAngleOrder, EulerAxis

q = Quaternion(0.675, 0.42, 0.5, 0.71)

# Quaternion -> RotationMatrix -> EulerAngle -> EulerAxis -> Quaternion
r = q.to_rotation_matrix()
e = r.to_euler_angle(EulerAngleOrder.ZYX)
ea = e.to_euler_axis()
q_back = ea.to_quaternion()

JAX Compatibility¶

All four types are registered as JAX pytrees and work with jax.jit:

import jax

@jax.jit
def rotate_and_convert(q):
    r = q.to_rotation_matrix()
    return r.to_euler_angle(EulerAngleOrder.XYZ)

q = Quaternion(0.675, 0.42, 0.5, 0.71)
e = rotate_and_convert(q)

The pytree structure for each type:

Type	Leaves	Auxiliary
`Quaternion`	`(data,)`	`None`
`RotationMatrix`	`(data,)`	`None`
`EulerAngle`	`(phi, theta, psi)`	`order`
`EulerAxis`	`(axis, angle)`	`None`