Constant of motionIn mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion. However, it is a mathematical constraint, the natural consequence of the equations of motion, rather than a physical constraint (which would require extra constraint forces). Common examples include energy, linear momentum, angular momentum and the Laplace–Runge–Lenz vector (for inverse-square force laws). Constants of motion are useful because they allow properties of the motion to be derived without solving the equations of motion.
Stress–energy–momentum pseudotensorIn the theory of general relativity, a stress–energy–momentum pseudotensor, such as the Landau–Lifshitz pseudotensor, is an extension of the non-gravitational stress–energy tensor that incorporates the energy–momentum of gravity. It allows the energy–momentum of a system of gravitating matter to be defined. In particular it allows the total of matter plus the gravitating energy–momentum to form a conserved current within the framework of general relativity, so that the total energy–momentum crossing the hypersurface (3-dimensional boundary) of any compact space–time hypervolume (4-dimensional submanifold) vanishes.
Transformation infinitésimaleEn mathématique, une transformation infinitésimale est une petite transformation dans le sens où l'approximation au premier ordre est valable. Par exemple, pour un groupe à un paramètre agissant sur un espace de dimension finie, on aura où ε est un paramètre de la transformation, In la matrice identité de dimension n et A une matrice appelée générateur de la transformation. En général, une transformation T(ε) n'est pas linéaire, mais si son approximation au premier ordre est valable, alors elle s'écrit comme une somme de matrices.
