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Triad Method
The TRIAD method is the earliest published algorithm for Spacecraft attitude determination, determining spacecraft attitude, which was first introduced by Harold Black in 1964. Given the knowledge of two vectors in the reference and body coordinates of a satellite, the TRIAD algorithm obtains the direction cosine matrix relating to both frames. Harold Black played a key role in the development of the guidance, navigation, and control of the U.S. Navy's Transit satellite system at Johns Hopkins Applied Physics Laboratories. TRIAD represented the state of practice in spacecraft attitude determination before the advent of Wahba's problem and its several optimal solutions. Covariance analysis for Black's solution was subsequently provided by Markley. Summary Firstly, one considers the linearly independent reference vectors \vec_ and \vec_2 . Let \vec_1, \vec_2 be the corresponding measured directions of the reference unit vectors as resolved in a body fixed frame of reference. Followi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacecraft Attitude Determination
Spacecraft attitude control is the process of controlling the orientation of a spacecraft (vehicle or satellite) with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, etc. Controlling vehicle attitude requires actuators to apply the torques needed to orient the vehicle to a desired attitude, and algorithms to command the actuators based on the current attitude and specification of a desired attitude. Before and during attitude control can be performed, spacecraft attitude determination must be performed, which requires sensors for absolute or relative measurement. The broader integrated field that studies the combination of sensors, actuators and algorithms is called ''guidance, navigation and control'', which also involves non-attitude concepts, such as position determination and navigation. Motivation A spacecraft's attitude must typically be stabilized and controlled for a variety of reasons. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Matrix
In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is Q^\mathrm Q = Q Q^\mathrm = I, where is the transpose of and is the identity matrix. This leads to the equivalent characterization: a matrix is orthogonal if its transpose is equal to its inverse: Q^\mathrm=Q^, where is the inverse of . An orthogonal matrix is necessarily invertible (with inverse ), unitary (), where is the Hermitian adjoint ( conjugate transpose) of , and therefore normal () over the real numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix preserves the inner product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation, reflection or rotoreflection. In other words, it is a unitary transformation. The set of orthogonal matrices, under multiplication, forms the group , known as th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthonormality
In linear algebra, two vector space, vectors in an inner product space are orthonormal if they are orthogonality, orthogonal unit vectors. A unit vector means that the vector has a length of 1, which is also known as normalized. Orthogonal means that the vectors are all perpendicular to each other. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis (linear algebra), basis is called an ''orthonormal basis''. Intuitive overview The construction of orthogonality of vectors is motivated by a desire to extend the intuitive notion of perpendicular vectors to higher-dimensional spaces. In the Cartesian coordinate system#Cartesian coordinates in two dimensions, Cartesian plane, two Vector (geometry), vectors are said to be ''perpendicular'' if the angle between them is 90° (i.e. if they form a right angle). This definition can be formalized in Cartesian space by defining the dot produc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Attitude Dynamics And Control
Spacecraft attitude control is the process of controlling the orientation of a spacecraft (vehicle or satellite) with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, etc. Controlling vehicle attitude requires actuators to apply the torques needed to orient the vehicle to a desired attitude, and algorithms to command the actuators based on the current attitude and specification of a desired attitude. Before and during attitude control can be performed, spacecraft attitude determination must be performed, which requires sensors for absolute or relative measurement. The broader integrated field that studies the combination of sensors, actuators and algorithms is called '' guidance, navigation and control'', which also involves non-attitude concepts, such as position determination and navigation. Motivation A spacecraft's attitude must typically be stabilized and controlled for a variety of reasons. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orientation (geometry)
In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a Line (geometry), line, plane (geometry), plane or rigid body – is part of the description of how it is placed in the Euclidean space, space it occupies. More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement, in which case it may be necessary to add an imaginary translation (geometry), translation to change the object's position (geometry), position (or linear position). The position and orientation together fully describe how the object is placed in space. The above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its position does not change when it rotates. Euler's rotation theorem shows that in three dimensions any orien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacecraft Attitude Control
Spacecraft attitude control is the process of controlling the orientation of a spacecraft (vehicle or satellite) with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, etc. Controlling vehicle attitude requires actuators to apply the torques needed to orient the vehicle to a desired attitude, and algorithms to command the actuators based on the current attitude and specification of a desired attitude. Before and during attitude control can be performed, spacecraft attitude determination must be performed, which requires sensors for absolute or relative measurement. The broader integrated field that studies the combination of sensors, actuators and algorithms is called ''guidance, navigation and control'', which also involves non-attitude concepts, such as position determination and navigation. Motivation A spacecraft's attitude must typically be stabilized and controlled for a variety of reasons. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
