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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 same point.
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
A force on an extended rigid body is a sliding vector. non-rigid extended. The point of application of a force becomes crucial and has to be indicated on the diagram. A force on a non-rigid body is a bound vector. Some use the tail of the arrow to indicate the point of application. Others use the tip.
This procedure can be repeated to add F 3 to the resultant F 1 + F 2, and so forth. The parallelogram of forces is a method for solving (or visualizing) the results of applying two forces to an object. When more than two forces are involved, the geometry is no longer a parallelogram, but the same principles apply to a polygon of forces.
If point A has velocity components = (,,) and point B has velocity components = (,,) then the velocity of point A relative to point B is the difference between their components: / = = (,,) Alternatively, this same result could be obtained by computing the time derivative of the relative position vector r B/A .
The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original system of forces. [ 1 ]
The method starts by guessing somehow the values of y at all grid points t k with 0 ≤ k ≤ N − 1. Denote these guesses by y k. Let y(t; t k, y k) denote the solution emanating from the kth grid point, that is, the solution of the initial value problem ′ = (, ()), =.