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The ancient Greek understanding of physics was limited to the statics of simple machines (the balance of forces), and did not include dynamics or the concept of work. During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading ...
The work of a force on a particle along a virtual displacement is known as the virtual work. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, [ 1 ] but they have also been developed for the study of the mechanics of deformable bodies.
In the application of the principle of virtual work it is often convenient to obtain virtual displacements from the velocities of the system. For the n particle system, let the velocity of each particle P i be V i, then the virtual displacement δr i can also be written in the form [2] = = ˙, =, …,.
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 .
The principle asserts for N particles the virtual work, i.e. the work along a virtual displacement, δr k, is zero: [9] = (+) = The virtual displacements , δ r k , are by definition infinitesimal changes in the configuration of the system consistent with the constraint forces acting on the system at an instant of time , [ 22 ] i.e. in such a ...
Castigliano's method for calculating displacements is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q i then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q i in the direction of Q i.
Every conservative force has a potential energy. By following two principles one can consistently assign a non-relative value to U: Wherever the force is zero, its potential energy is defined to be zero as well. Whenever the force does work, potential energy is lost.
The most common example is in a vehicle's suspension, where it is used to describe the displacement and forces in the springs and shock absorbers. The force in the spring is (roughly) the vertical force at the contact patch divided by the motion ratio, and the spring rate is the wheel rate divided by the motion ratio squared.