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Attitude

The attitude module contains function for common attitude operations, different attitude representations (Quaternions, Euler Angles, Euler Axis & Angle, Rotation Matrices), and transformations between different attitude representations.

SatelliteDynamics.Rx — Function

Rotation matrix, for a rotation about the x-axis.

Arguments:

  • angle::Real: Counter-clockwise angle of rotation as viewed looking back along the postive direction of the rotation axis.
  • use_degrees:Bool: If true interpret input as being in degrees.

Returns:

  • r::Array{<:Real, 2}: Rotation matrix

References:

  1. O. Montenbruck, and E. Gill, Satellite Orbits: Models, Methods and Applications, 2012, p.27.
source
SatelliteDynamics.Ry — Function

Rotation matrix, for a rotation about the y-axis.

Arguments:

  • angle::Real: Counter-clockwise angle of rotation as viewed looking back along the postive direction of the rotation axis.
  • use_degrees:Bool: If true interpret input as being in degrees.

Returns:

  • r::Array{<:Real, 2}: Rotation matrix

References:

  1. O. Montenbruck, and E. Gill, Satellite Orbits: Models, Methods and Applications, 2012, p.27.
source
SatelliteDynamics.Rz — Function

Rotation matrix, for a rotation about the z-axis.

Arguments:

  • angle::Real: Counter-clockwise angle of rotation as viewed looking back along the postive direction of the rotation axis.
  • use_degrees:Bool: If true interpret input as being in degrees.

Returns:

  • r::Array{<:Real, 2}: Rotation matrix

References:

  1. O. Montenbruck, and E. Gill, Satellite Orbits: Models, Methods and Applications, 2012, p.27.
source

Quaternions

SatelliteDynamics.Quaternion — Type

The Quaternion type defines a scalar-first quaternion for representation of attitude.

Data members:

  • q0::Float64: Scalar part of quaternion
  • q1::Float64: First vector component of quaternion
  • q2::Float64: Second vector component of quaternion
  • q3::Float64: Third vector component of quaternion

References:

  1. J. Diebel, Representing attitude: Euler angles, unit quaternions, and rotation vectors. Matrix 58(15-16) (2006).
source
SatelliteDynamics.as_vector — Function

Return quaternion as a vector.

Equivalent to q[:]

Arguments:

  • q::Quaternion: Quaternion

Returns:

  • vec::Array{Float64, 1}: Quaternion as a (4,) vector
source

Return Euler angles as a vector.

Equivalent to: [e.phi, e.theta, e.psi] for EulerAngle e

Arguments:

  • e::EulerAngle Euler Angle

Returns:

  • evec::Array{Float64, 1} Euler angles components in vector form.
source
SatelliteDynamics.as_matrix — Function

Return the rotation matrix representation of a Quaternion.

Arguments:

  • q::Quaternion: Quaternion

Returns:

  • mat::Array{Float64, 2}: Rotation Matrix on SO(3).
source
SatelliteDynamics.slerp — Function

Perform spherical linear interpolation (SLERP) on two quaternions. Interpolatles from quaternion, q1, to quaternion, q2, at normalized interpolation time, t.

Interpolation time must be in the range [0, 1] a value of 0 will return q1, while a value of 1 will return q2.

Arguments:

  • q1::Quaternion: Starting Quaternion
  • q2::Quaternion: Ending Quaternion
  • t::Real: Normalized interpolation time. [0, 1]

Returns:

  • q:Quaternion: Quaternion attitude interpolation from q1 toward q2 at time t.
source

EulerAngle

SatelliteDynamics.EulerAngle — Type

The EulerAngle type provides a represenation of EulerAngles for storing attitude information.

Valid sequences are: 121, 123, 131, 132, 212, 213, 231, 232, 312, 313, 321, 323.

Data members:

  • seq::Integer: Order of application of angles with respect to body axis.
  • phi::Float64: First Euler angle
  • theta::Float64: Second Euler angle
  • psi::Float64: Third Euler angle

References:

  1. J. Diebel, Representing attitude: Euler angles, unit quaternions, and rotation vectors. Matrix 58(15-16) (2006).
source

EulerAxis

SatelliteDynamics.EulerAxis — Type

The EulerAxis type provides a representation of the Euler angle-and-axis attitude representation.

Data members:

  • theta::Float64: Angle of rotation
  • vec::Array{Float64, 1}: Axis of rotation

References:

  1. J. Diebel, Representing attitude: Euler angles, unit quaternions, and rotation vectors. Matrix 58(15-16) (2006).
source