State Vector (geographical)
In navigation, a state vector is a set of data describing exactly where an object is located in space, and how it is moving. Mathematical representation A state vector typically will contain seven elements: three position coordinates, three velocity terms, and the time at which these values were valid. Mathematically, in order to describe positions in a N-dimensional space ( \mathbb^N ) then a state vector \textbf belongs to \mathbb^: \mathbf(t) = \begin x_1(t)\\ x_2 (t)\\ x_3(t) \\ v_1(t) \\ v_2 (t) \\ v_3 (t) \end or simply \mathbf(t) = \begin \mathbf(t) \\ \mathbf(t)\end where \mathbf = \begin x_1 & x_2 & x_3 \end^\mathsf is the position vector and \mathbf = \dot = \begin v_1 & v_2 & v_3 \end^\mathsf{T} is the velocity vector. Since there is freedom to choose coordinate systems for position, a state vector may also be expressed in a variety of coordinate systems (e.g. the North east down coordinate system). See also *Orbital state vectors In astrodynamics and ce ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Position (vector)
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point ''P'' in space. Its length represents the distance in relation to an arbitrary reference origin ''O'', and its direction represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from ''O'' to ''P''. In other words, it is the displacement or translation that maps the origin to ''P'': :\mathbf=\overrightarrow. The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus. Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension.Keller, F. J., Gettys, W. E. et al. (1993), p. 28–29. Relative position The relative position of a point ''Q'' with respect to point ''P'' is the Euclidean vector res ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Velocity
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical quantity, quantity, meaning that both magnitude and direction are needed to define it. The Scalar (physics), scalar absolute value (Magnitude (mathematics), magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the International System of Units, SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an ''acceleration''. Definition Average velocity The average velocity of an object over a period of time is its Displacement (geometry), change in position, \Delta s, divided by the duration of the period, \Delt ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Time
Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequence events, to compare the duration of events (or the intervals between them), and to quantify rates of change of quantities in material reality or in the qualia, conscious experience. Time is often referred to as a fourth dimension, along with Three-dimensional space, three spatial dimensions. Time is one of the seven fundamental physical quantities in both the International System of Units (SI) and International System of Quantities. The SI base unit of time is the second, which is defined by measuring the electronic transition frequency of caesium atoms. General relativity is the primary framework for understanding how spacetime works. Through advances in both theoretical and experimental investigations of spacetime, it has been shown ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Coordinate System
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they are commonly distinguished by their position in an ordered tuple, or by a label, such as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the '' number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate o ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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North East Down
Local tangent plane coordinates (LTP) are part of a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. They are also known as local ellipsoidal system, local geodetic coordinate system, local vertical, local horizontal coordinates (LVLH), or topocentric coordinates. It consists of three coordinates: one represents the position along the northern axis, one along the local eastern axis, and one represents the vertical position. Two right-handed variants exist: east, north, up (ENU) coordinates and north, east, down (NED) coordinates. They serve for representing state vectors that are commonly used in aviation and marine cybernetics. Axes These frames are location dependent. For movements around the globe, like air or sea navigation, the frames are defined as tangent to the lines of geographical coordinates: *East–west tangent to parallels, *North–south tangent to meridians, and *Up–down in the di ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Orbital State Vectors
In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are cartesian coordinate system, Cartesian vectors of position (vector), position (\mathbf) and velocity (\mathbf) that together with their time (epoch (astronomy), epoch) (t) uniquely determine the trajectory of the orbiting body in space. Orbital state vectors come in many forms including the traditional Position-Velocity vectors, Two-line element set (TLE), and Vector Covariance Matrix (VCM). Frame of reference State vectors are defined with respect to some frame of reference, usually but not always an inertial reference frame. One of the more popular reference frames for the state vectors of bodies moving near Earth is the Earth-centered inertial (ECI) system defined as follows: *The origin (geometry), origin is Earth's center of mass; *The Z axis is coincident with Earth's rotational axis, positive northward; *The X/Y plane coincides with Earth's equatorial plane, with th ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |