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Two intersecting lines. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection.
A two-dimensional Poincaré section of the forced Duffing equation. In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.
The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position x {\displaystyle x} , which varies with t {\displaystyle t} (time).
Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period. For a function on the real numbers or on the integers , that means that the entire graph can be formed from copies of one particular portion, repeated at regular intervals.
The idea of reducing geometry to its characteristic group was developed particularly by Mario Pieri in his reduction of the primitive notions of geometry to merely point and motion. Hyperbolic motions are often taken from inversive geometry : these are mappings composed of reflections in a line or a circle (or in a hyperplane or a hypersphere ...
Animation for Peaucellier–Lipkin linkage: Dimensions: Cyan Links = a Green Links = b Yellow Links = c. The Peaucellier–Lipkin linkage (or Peaucellier–Lipkin cell, or Peaucellier–Lipkin inversor), invented in 1864, was the first true planar straight line mechanism – the first planar linkage capable of transforming rotary motion into perfect straight-line motion, and vice versa.
Irrational windings are also examples of the fact that the topology of the submanifold does not have to coincide with the subspace topology of the submanifold. [ 2 ] Secondly, the torus can be considered as a Lie group U ( 1 ) × U ( 1 ) {\displaystyle U(1)\times U(1)} , and the line can be considered as R {\displaystyle \mathbb {R} } .
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by ...