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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The generating function F for this transformation is of the third kind, = (,). To find F explicitly, use the equation for its derivative from the table above, =, and substitute the expression for P from equation , expressed in terms of p and Q:
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
List of equations in nuclear and particle physics; ... Physics for Scientists and Engineers: With Modern Physics (6th ed.). W.H. Freeman and Co. ISBN ...
In physics, Hooke inferred that gravity obeys an inverse square law and arguably was the first to hypothesise such a relation in planetary motion, [19] [20] a principle Isaac Newton furthered and formalised in Newton's law of universal gravitation. [21] Priority over this insight contributed to the rivalry between Hooke and Newton.
A neo-Hookean solid [1] [2] is a hyperelastic material model, similar to Hooke's law, that can be used for predicting the nonlinear stress–strain behavior of materials undergoing large deformations.
Restricted canonical transformations are coordinate transformations where transformed coordinates Q and P do not have explicit time dependence, i.e., = (,) and = (,).The functional form of Hamilton's equations is ˙ =, ˙ = In general, a transformation (q, p) → (Q, P) does not preserve the form of Hamilton's equations but in the absence of time dependence in transformation, some ...
Employing atomic units, the Hamiltonian defining the Hooke's atom is ^ = + (+) + | |. As written, the first two terms are the kinetic energy operators of the two electrons, the third term is the harmonic electron-nucleus potential, and the final term the electron-electron interaction potential.