attitude

Implements the yaw steering control law for solar panel optimization.

Functions¶

`calculate_yaw_steering`¶

Calculate optimal yaw angle for given sun position.

def calculate_yaw_steering(
    orbit: EquatorialOrbit,
    t: float,
    sun_eci: tuple[float, float, float]
) -> AttitudeSolution:

Parameters:

orbit: EquatorialOrbit instance
t: Time since epoch [s]
sun_eci: Sun direction in ECI frame

Returns: AttitudeSolution with yaw and beta angles.

Algorithm¶

Step 1: Transform Sun to LVLH¶

Get LVLH basis and project sun vector:

\[ \mathbf{s}_{\text{local}} = \begin{bmatrix} \mathbf{s} \cdot \mathbf{x}_L \\ \mathbf{s} \cdot \mathbf{y}_L \\ \mathbf{s} \cdot \mathbf{z}_L \end{bmatrix} \]

Step 2: Calculate Yaw Angle¶

Rotation about nadir (Z) axis:

\[ \boxed{\psi = \arctan2(s_{y,\text{local}}, s_{x,\text{local}})} \]

This places the sun vector in the body X-Z plane.

Step 3: Calculate Beta Angle¶

Sun elevation above orbital plane:

\[ \beta = \arcsin(-s_{y,\text{local}}) \]

Physical Interpretation¶

Condition	Yaw \(\psi\)	Meaning
Sun ahead	0°	Face forward
Sun behind	180°	Face backward
Sun at ±90°	±90°	Rotate sideways

Implementation¶

def calculate_yaw_steering(orbit, t, sun_eci):
    # Normalize sun vector
    s_eci = np.array(sun_eci) / np.linalg.norm(sun_eci)

    # Get LVLH basis
    x_lvlh, y_lvlh, z_lvlh = orbit.get_lvlh_basis(t)

    # Project to local frame
    sx_local = np.dot(s_eci, x_lvlh)
    sy_local = np.dot(s_eci, y_lvlh)
    sz_local = np.dot(s_eci, z_lvlh)

    # Yaw and beta
    psi = np.arctan2(sy_local, sx_local)
    beta = np.arcsin(-sy_local)

    return AttitudeSolution(t=t, yaw=psi, beta=beta, ...)