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The S-matrix is closely related to the transition probability amplitude in quantum mechanics and to cross sections of various interactions; the elements (individual numerical entries) in the S-matrix are known as scattering amplitudes. Poles of the S-matrix in the complex-energy plane are identified with bound states, virtual states or resonances.
In S-matrix theory, the S-matrix relates the infinite past to the infinite future in one step, without being decomposable into intermediate steps corresponding to time-slices. This program was very influential in the 1960s, because it was a plausible substitute for quantum field theory , which was plagued with the zero interaction phenomenon at ...
The components of [S] are the components of the twist screw, and for this reason [S] is also often called a twist. From the definition of the matrix [S], we can formulate the ordinary differential equation, [˙ ()] = [] [()], and ask for the movement [T(t)] that has a constant twist matrix [S]. The solution is the matrix exponential
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments ) acting on the rigid body.
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is
There are several different methods available for evaluating a matrix equation including but not limited to Cholesky decomposition and the brute force evaluation of systems of equations. If a structure isn’t properly restrained, the application of a force will cause it to move rigidly and additional support conditions must be added.
Lorentz force acting on fast-moving charged particles in a bubble chamber.Positive and negative charge trajectories curve in opposite directions. In physics, specifically in electromagnetism, the Lorentz force law is the combination of electric and magnetic force on a point charge due to electromagnetic fields.
Flexibility is the inverse of stiffness.For example, consider a spring that has Q and q as, respectively, its force and deformation: . The spring stiffness relation is Q = k q where k is the spring stiffness.