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In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors.
In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
The finiteness of the set of three-point central configurations was shown by Joseph-Louis Lagrange in his solution to the three-body problem; Lagrange showed that there is only one non-collinear central configuration, in which the three points form the vertices of an equilateral triangle.
(L3) at least dimension 2 if it has at least 3 non-collinear points (or two lines, or a line and a point not on the line), (L4) at least dimension 3 if it has at least 4 non-coplanar points. The maximum dimension may also be determined in a similar fashion. For the lowest dimensions, they take on the following forms. A projective space is of:
The fact that coordinate axes are non-parallel in this construction after two consecutive non-collinear boosts is a precise expression of the phenomenon of Thomas rotation. [nb 1] The velocity of Σ′′ as seen in Σ is denoted w d = u ⊕ v, where ⊕ refers to the relativistic addition of velocity (and not ordinary vector addition), given ...
[12] An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259 [ 13 ] 20 examples of periodic solutions to the three-body problem In the 1970s, Michel Hénon and Roger A. Broucke each found a set of solutions that form part of the same family of solutions: the Broucke–Hénon–Hadjidemetriou family.
In engineering, a parallel force system is a type of force system where in all forces are oriented along one axis. An example of this is a see saw . The children are applying the two forces at the ends, and the fulcrum in the middle gives the counter force to maintain the see saw in neutral position.
A single force acting at any point O′ of a rigid body can be replaced by an equal and parallel force F acting at any given point O and a couple with forces parallel to F whose moment is M = Fd, d being the separation of O and O′. Conversely, a couple and a force in the plane of the couple can be replaced by a single force, appropriately ...