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Coplanarity. 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.
Lami's theorem. 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. According to the theorem, {\displaystyle {\frac {v_ {A}} {\sin \alpha }}= {\frac {v_ {B}} {\sin ...
A shearing force is applied to the top of the rectangle while the bottom is held in place. The resulting shear stress, τ, deforms the rectangle into a parallelogram. The area involved would be the top of the parallelogram. Shear stress (often denoted by τ, Greek: tau) is the component of stress coplanar with a material cross section.
Varignon's theorem (mechanics) Varignon's theorem is a theorem of French mathematician Pierre Varignon (1654–1722), published in 1687 in his book Projet d'une nouvelle mécanique. The theorem states that the torque of a resultant of two concurrent forces about any point is equal to the algebraic sum of the torques of its components about the ...
Lagrangian. [edit] Instead of forces, Lagrangian mechanics uses the energies in the system. The central quantity of Lagrangian mechanics is the Lagrangian, a function which summarizes the dynamics of the entire system. Overall, the Lagrangian has units of energy, but no single expression for all physical systems.
The Lagrange points can then be seen as the five places where the gradient on the resultant surface is zero, indicating that the forces are in balance there. [citation needed] In the restricted three-body problem, a body of negligible mass (the "planetoid") moves under the influence of two massive bodies. Having negligible mass, the planetoid ...
v. t. e. Mechanics of planar particle motion[1] is the analysis of the motion of particles gravitationally attracted to one another which are observed from non-inertial reference frames [2][3][4] and the generalization of this problem to planetary motion. [5] This type of analysis is closely related to centrifugal force, two-body problem, orbit ...
A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance or moment. The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coincide. This is called a "simple couple". [1] The forces have a turning effect or moment called a torque about an axis ...