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Numerical relativity. Numerical relativity is the sub-field of general relativity which seeks to solve Einstein's equations through the use of numerical methods. Finite difference, finite element and pseudo-spectral methods are used to approximate the solution to the partial differential equations which arise.
Voronoi formula. In mathematics, a Voronoi formula is an equality involving Fourier coefficients of automorphic forms, with the coefficients twisted by additive characters on either side. It can be regarded as a Poisson summation formula for non-abelian groups. The Voronoi (summation) formula for GL (2) has long been a standard tool for ...
Equations for a falling body. A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth -bound conditions. Assuming constant acceleration g due to Earth’s gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth’s ...
Action principles lie at the heart of fundamental physics, from classical mechanics through quantum mechanics, particle physics, and general relativity. [1] Action principles start with an energy function called a Lagrangian describing the physical system. The accumulated value of this energy function between two states of the system is called ...
Ginzburg–Landau theory. In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Inverse rigid-body dynamics is a method for computing forces and/or moments of force (torques) based on the kinematics (motion) of a body and the body's inertial properties (mass and moment of inertia). Typically it uses link-segment models to represent the mechanical behaviour of interconnected segments, such as the limbs of humans [1] or ...
The Frenet–Serret formulas were generalized to higher-dimensional Euclidean spaces by Camille Jordan in 1874. Suppose that r(s) is a smooth curve in and that the first n derivatives of r are linearly independent. [2] The vectors in the Frenet–Serret frame are an orthonormal basis constructed by applying the Gram-Schmidt process to the ...