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In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. [1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory .
A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration. The distance between any two particles changes if and only if deformation has occurred. If displacement occurs without deformation, then it is a rigid-body displacement.
When the rays are lines of sight from an observer to two points in space, it is known as the apparent distance or apparent separation. Angular distance appears in mathematics (in particular geometry and trigonometry ) and all natural sciences (e.g., kinematics , astronomy , and geophysics ).
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Subtraction of two vectors can be geometrically illustrated as follows: to subtract b from a, place the tails of a and b at the same point, and then draw an arrow from the head of b to the head of a. This new arrow represents the vector (-b) + a, with (-b) being the opposite of b, see drawing. And (-b) + a = a − b. The subtraction of two ...
Relative velocities between two particles in classical mechanics. The figure shows two objects A and B moving at constant velocity. The equations of motion are: = +, = +, where the subscript i refers to the initial displacement (at time t equal to zero).
Parallel plane segments with the same orientation and area corresponding to the same bivector a ∧ b. [1]In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors.
Particle displacement, a measurement of distance of the movement of a particle in a medium as it transmits a wave (represented in mathematics by the lower-case Greek letter ξ) Displacement field (mechanics), an assignment of displacement vectors for all points in a body that is displaced from one state to another