Chapter 4. A Damped Oscillator Model of Relativistic Dynamics in Rapidity Space


R.M. Yamaleev
Joint Institute for Nuclear Research, LIT, Dubna, Russia

Part of the book: Future Relativity, Gravitation, Cosmology


The second order polynomial relationship between energy, mass and momentum, the mass-shell equation, is considered as the characteristic polynomial of the second order ordinary differential equation describing the damped oscillator model. It is shown, the quotient of two fundamental solutions of the differential equation describes an evolution of the energy and momentum of the relativistic particle with respect to hyperbolic and periodic angles. A geometrical interpretation is done within the framework of hyperbolic and elliptic geometries. Transitions between different kinds of the evolution parameters are interpreted as passes from one system of references onto the other. Evolution equations covariant with respect to these transitions are formulated within the framework of Jacobi elliptic functions.


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