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In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non- quantum mechanical description of a system of particles, or of a fluid , in cases where the velocities of moving objects are comparable to the speed of light c .
Vladimir Karapetoff (1944) "The special theory of relativity in hyperbolic functions", Reviews of Modern Physics 16:33–52, Abstract & link to pdf Lanczos, Cornelius (1949), The Variational Principles of Mechanics , University of Toronto Press , pp. 304–312 Also used biquaternions.
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields.
Fluid Mechanics. Vol. 6 (2nd ed.). Butterworth-Heinemann. ISBN 978-0-08-033933-7. Volume 6 covers fluid mechanics in a condensed but varied exposition, from ideal to viscous fluids, includes a chapter on relativistic fluid mechanics, and another on superfluids.
The relativistic Lagrangian can be derived in relativistic mechanics to be of the form: = (˙) (, ˙,). Although, unlike non-relativistic mechanics, the relativistic Lagrangian is not expressed as difference of kinetic energy with potential energy, the relativistic Hamiltonian corresponds to total energy in a similar manner but without including rest energy.
Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them (e.g. the Dirac or path-integral formalism) also work with special relativity.
The special theory of relativity enjoys a relationship with electromagnetism and mechanics; that is, the principle of relativity and the principle of stationary action in mechanics can be used to derive Maxwell's equations, [7] [8] and vice versa.