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Pole figure and diffraction figure. Consider the diffraction pattern obtained with a single crystal, on a plane that is perpendicular to the beam, e.g. X-ray diffraction with the Laue method, or electron diffraction in a transmission electron microscope. The diffraction figure shows spots. The position of the spots is determined by the Bragg's ...
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.) Momentum space is the set of all momentum ...
A two-line element set (TLE, or more rarely 2LE) or three-line element set (3LE) is a data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the epoch. Using a suitable prediction formula, the state (position and velocity) at any point in the past or future can be estimated to some accuracy.
The trajectory of a point can be written as a function of time as {ξ 10 + ω 1 t, η 0, ξ 20 + ω 2 t} and stereographically projected onto its associated torus, as in the figures below. [8] In these figures, the initial point is taken to be {0, π / 4 , 0}, i.e. on the Clifford torus. In Fig. 1, two simple rotation trajectories are ...
For example, the orientation in space of a line, line segment, or vector can be specified with only two values, for example two direction cosines. Another example is the position of a point on the Earth, often described using the orientation of a line joining it with the Earth's center, measured using the two angles of longitude and latitude.
There can be two types of singularities of the n-body problem: collisions of two or more bodies, but for which q(t) (the bodies' positions) remains finite. (In this mathematical sense, a "collision" means that two pointlike bodies have identical positions in space.) singularities in which a collision does not occur, but q(t) does not remain ...
The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector , the state vector . If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.