2020•Applied MathematicsOpen access

Noncovariant Lagrangians Are Presented Which Yield Two-Component Equations of Motion for a Class of Relativistic Mechanical Systems in 1 + 1 Dimensions Including the Harmonic Oscillator

R. L. Anderson

Abstract

First, a Lagrangian is presented and authenticated for a Relativistic Harmonic Oscillator in 1 + 1 dimensions. It yields a two-component set of equations of motion. The time-component is the missing piece in all previous discussions of this system! The second result is that this Oscillator Langrangian generalizes to Langrangians for a class of particles in 1 + 1 dimensions subject to an arbitrary potential V which is space dependent only.

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Key concepts: Harmonic oscillator, Lagrangian, Component (thermodynamics), Equations of motion, Motion (physics), Class (philosophy), Simple harmonic motion, Harmonic