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Lecture# Relativistic Dynamics Overview

Description

This lecture introduces the concept of four-vectors in space-time, focusing on the quadri-vector energy-momentum and its transformation when changing the frame of reference. It discusses the kinetic energy plus a specific term, the 'mass condition', and properties like energy conservation and the kinetic energy theorem in the context of relativistic dynamics.

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Related concepts (32)

In MOOCs (9)

Four-momentum

In special relativity, four-momentum (also called momentum–energy or momenergy) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle with relativistic energy E and three-momentum p = (px, py, pz) = γmv, where v is the particle's three-velocity and γ the Lorentz factor, is The quantity mv of above is ordinary non-relativistic momentum of the particle and m its rest mass.

Four-vector

In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (1/2,1/2) representation. It differs from a Euclidean vector in how its magnitude is determined.

Four-velocity

In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space. Physical events correspond to mathematical points in time and space, the set of all of them together forming a mathematical model of physical four-dimensional spacetime. The history of an object traces a curve in spacetime, called its world line.

Four-current

In special and general relativity, the four-current (technically the four-current density) is the four-dimensional analogue of the electric current density. Also known as vector current, it is used in the geometric context of four-dimensional spacetime, rather than three-dimensional space and time separately. Mathematically it is a four-vector, and is Lorentz covariant. Analogously, it is possible to have any form of "current density", meaning the flow of a quantity per unit time per unit area.

Energy–momentum relation

In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum. It can be written as the following equation: This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m0, and momentum of magnitude p; the constant c is the speed of light.

Ce cours de Physique générale – mécanique fourni les outils permettant de maîtriser la mécanique newtonienne du point matériel.

Ce cours de Physique générale – mécanique fourni les outils permettant de maîtriser la mécanique newtonienne du point matériel.

Ce cours de Physique générale – mécanique fourni les outils permettant de maîtriser la mécanique newtonienne du point matériel.

Ces quelques leçons de mécanique de Newton font partie d'un cours de formation de base en mécanique Newtonienne présenté sous la forme de 5 MOOCs:

- Mécanique de Newton
- Mécanique du point matérie

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