Module utils

Utility functions shared by different modules, and which may be useful to engineers.

Functions

are_eigenvalues_stable

Checks if the given matrix represents a stable linear system by examining its eigenvalues.

between_0_360

Returns the provided angle bounded between 0.0 and 360.0.

between_pm_180

Returns the provided angle bounded between -180.0 and +180.0

between_pm_x

Returns the provided angle bounded between -x and +x.

capitalize

Capitalize the first letter of a string

cartesian_to_spherical

Converts the input vector V from Cartesian coordinates to spherical coordinates Returns ρ, θ, φ where the range ρ is in the units of the input vector and the angles are in radians

denormalize

Denormalize a value between -1.0 and 1.0

is_diagonal

Checks if the provided 3x3 matrix is diagonal.

kronecker

The Kronecker delta function

mag_order

Returns the order of mangitude of the provided value

normalize

Normalize a value between -1.0 and 1.0

perpv

Returns the components of vector a orthogonal to b

projv

Returns the projection of a onto b

r1

Returns a rotation matrix for a rotation about the X axis.

r2

Returns a rotation matrix for a rotation about the Y axis.

r3

Returns a rotation matrix for a rotation about the Z axis.

rotv

Rotate a vector about a given axis

rss_errors

Computes the Root Sum Squared (RSS) state errors between two provided vectors.

rss_orbit_errors

Computes the Root Sum Squared (RSS) orbit errors in kilometers and kilometers per second.

rss_orbit_vec_errors

Computes the Root Sum Squared (RSS) state errors in position and in velocity of two orbit vectors [P V].

spherical_to_cartesian

Converts the input vector V from Cartesian coordinates to spherical coordinates Returns ρ, θ, φ where the range ρ is in the units of the input vector and the angles are in radians

tilde_matrix

Returns the skew-symmetric matrix (also known as the tilde matrix) corresponding to the provided 3D vector.

unitize

Returns the unit vector of the moved input vector